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Board
/sci/ - Science & Math

Previously >>14991217

>what is /sqt/ for?
Questions regarding maths and science. Also homework.
>where do I go for advice?
>where do I go for other questions and requests?
>>>/wsr/ >>>/g/sqt >>>/diy/sqt etc.
>how do I post math symbols (Latex)?
rentry.org/sci-latex-v1
>a plain google search didn't return anything, is there anything else I should try before asking the question here?
>where can I search for proofs?
proofwiki.org
>where can I look up if the question has already been asked here?
warosu.org/sci
eientei.xyz/sci
>how do I optimize an image losslessly?
trimage.org
pnggauntlet.com
>how do I find the source of an image?
tineye.com
saucenao.com
iqdb.org

>where can I get:
>books?
libgen.rs
z-lib.org
stitz-zeager.com
openstax.org
activecalculus.org
>articles?
sci-hub.st
>book recs?
4chan-science.fandom.com/wiki//sci/_Wiki
>online courses and lectures?
>charts?
imgur.com/a/pHfMGwE
imgur.com/a/ZZDVNk1
>tables, properties and material selection?
www.engineeringtoolbox.com
www.matweb.com
www.chemspider.com

>attach an image (animal images are ideal, you can grab them from >>>/an/. Alternatively use anime from safebooru.donmai.us)
>recheck the Latex before posting
>ignore shitpost replies
>avoid getting into arguments
>do not tell us where is it you came from
>do not mention how [other place] didn't answer your question so you're reposting it here
>if you need to ask for clarification fifteen times in a row, try to make the sequence easy to read through
>I'm not flipping that sideways picture
>don't ask for a hint if you want a solution
>xyproblem.info
>>

Maths questions (inb4 "what the actual fuck"):
>>14992032
>>14994050 [Elaboration in >>14994054]
>>14996226
>>14996769
>>14997858
>>14997898
>>14998022
>>14998311
>>14998544
>>14999441
>>15001043
>>15002714
>>15003941

Engineering questions:
>>14999455

Medicine questions:
>>14994080
>>14997335

Chemistry questions:
>>14996225
>>14998891

Stupid questions:
>>14996644
>>14997040
>>14997574
>>14998595
>>14998678
>>15001111
>>15001152
>>15002686
>>15003097
>>15003827
>>
The slowerest /sqt/
>>
Is ARM the future of of microcontrollers? More broadly, is ARM the future? Is there no hope for RISC V?
>>
If I wanted to learn C++ as an absolute beginner, should I start with C first, then move on to C++? Or jump directly into C++?
>>
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>>15004641
i'm trying to find the solution to this recurrence, as homework. i have a test by monday.

a(n) = -2^(n - 2) (-4 c_1 + n + 1) + c_2 4^n + 1/3 (worfram alpha, do not have premium bc poor)
i'm getting:
a(n) = -2^(n - 2) (-4 c_1 + n) + c_2 4^n + 1/3

think i'm mistaken in finding the general form of the nonhomogenous part: 1 + 2^n

if someone could help me. i'm currently using "a + bn2^n" as general form
>>
>>15005117
either way works
>>
Is it better to represent a subcsript deduction as like

X1-2 or X1-X2?

(numbers are subscript but idk how into 4channel)
>>
>>15005132
which is easier and less time-consuming for an absolute beginner. I don't have a lot of spare time. I'd also have to deal with my college studies and job.
>>
>>15005188
if you want it fast just learn 1 (c++) instead both. you'll get used to it, you just need logics and algorithmic thinking, sintax is trivial

t. >>15005120
(if you could help me)
>>
>>15005117
I prefer C because I hate reading and love autistically churning out low level shit, but C++ is more convenient from a top-down approach
>>
>>15005120
It's the same thing. Just adjust the constant c_1.
>>
>>15005117
C will teach you more about coding and the fundamentals of computers, also why higher level languages exist. But if you want an easier time and be able to write programs quicker use C++. From my personal experience the best programmers I've known were all competent in C.
>>
>>14997040
Mine says max cool, so I assume yours is just an abbreviation of that. You could try putting a thermometer in and then switch it to the extremes and see.
>>
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>>15005117
Depends on what you want to do. If you just want to program you can start in any language.

Do you have a C++ specific goal?

C++ is just C with a bunch of unnecessary OOP stuff added in. If you want an interesting exercise, learn C and make your own data structures. You'll be effectively building your own C++ anyway and that way and you'll get an understanding of how object is formed and how it operates.

Alternatively if you'd rather play with objects than make them, look into Java. Java Collections are really nice for getting an OOP program running quickly and you don't have to care about pointers or other lower level things.

>Collections
https://docs.oracle.com/en/java/javase/18/docs/api/java.base/java/util/Collection.html

Whatever you pick, if it is a common language and can afford \$30/month, that is enough to license a professional IDE and get a built in AI assistant.

AI assistant is nice because a lot of times it reduces writing code to reading it's guess and pushing TAB if it guessed right.

Eventually it learns how you use it and ends up writing 60% of lines for you and your powers of development get extended and made faster.
>>
>>15005512
No one uses Java these days, at least not for new projects in the tech industry. Sure there is a huge legacy install base so it's not going anywhere but if you want to learn something future proof then avoid Java. There are many other languages that can teach OOP.
>>
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>>15005543
>No one uses Java these days, at least not for new projects in the tech industry.
This is just wrong.

>Sure there is a huge legacy install base so it's not going anywhere but if you want to learn something future proof then avoid Java.
No language is future proof. Languages which are powerful, widespread and and used in a lot of legacy code bases aren't even future proof. For example Rust is starting to show up places like the Linux kernel as a C replacement. I think Rust will probably eventually win and replace C most places. C is a better and more widespread language, but the Rust community has about 1000x more enthusiasm than the C one does, in a lot of the same spaces C is in. What gets used and where is ultimately decided by what community is actually capable/willing to make code for a problem and that is governed by the enthusiasm of the community.

Really if you want to be future proof as a programmer you just have to learn concepts and how to express them in whatever language you find yourself needing to use at the moment.

If you familiarize yourself with concepts like OOP or FP then learning a new language of either of those kinds is reduced to learning the quirks of your particular toolchain and the grammar of the language.

If you want to read about a trick I like, that simplifies that more, here is a pdf
http://www.gkc.org.uk/martin/papers/middle-out-t.pdf

>There are many other languages that can teach OOP.
This is true, but Java is the only modern language I really play with regularly and most anons won't think it is a useful task if I ask them to read a Modula-2 book, even if I tell them book is well-written and just consider Modula-2 examples as pseudocode and apply ideas wherever you want.
>>
>>15004278
pay attention to the variable w.r.t. which you are integrating. Here, that is 'x' so you can keep 'a' as constant.
>>
>>15005612
>C is a better and more widespread language, but the Rust community has about 1000x more enthusiasm than the C one does
That has nothing to do with the rise in popularity of Rust. Unlike C++ or Go, Rust *is* C but updated in a way to make it more modern, with hugely beneficial features such as compiler enforced thread safety and bounds checking. There is a reason no other language has made it into the Linux Kernel since it was first written until Rust. C has a whole bunch of problems and even experts in it make mistakes, Rust solves all of those problems while remaining low level enough to be used in kernel coding.
>>
>>15005097
ARM is more integrated and popular with the industry, but RISC V is better for self-learning the RISC architecture.

>>15005117
>>
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>>15005631
Rust's safety is a security theater at best. To make Rust do anything interesting or useful, you are putting that code in an unsafe block anyways. There are no real advantages to using it over C currently, and it has a nasty habit of making very large binaries for no good reason.

Currently, Rust is essentially a downgraded C.

It is being promoted places because it has an enthusiastic community of people who seem to exist just to make Rust code and post about it on the internet. Rust is more about having sort of a big online social club that makes a lot of projects and people are nice to each other more than anything else. If it replaces C, which it probably will if things remain stable, it is because of that. Not because of any merits of the actual language itself.

I don't say this to denigrate Rust. Making a nice community is a harder task than making a compiler and probably in the future someone will join the community who ends up making the security theater into the real deal and fixes the super huge binaries problem.

>tl;dr: A good large community is a much bigger power than a good programming language.
>>
>>15004641
What glass additives to turn infrared light into visible? High-res FLIR sensors are unnecessary expensive!
>>
>>15005650
>There are no real advantages to using it over C currently, and it has a nasty habit of making very large binaries for no good reason.
This just proves you have no idea what you're talking about or the technical reasons it is the only language other than C to be used in the Linux Kernel. Programming in the real world isn't a popularity contest.
>>
>>15005656
>about or the technical reasons it is the only language other than C to be used in the Linux Kernel.
There aren't any. It is in the Linux kernel because Rust users were numerous and loud enough to pressure a smaller community into doing what they want, and talented enough to working produce code.

>Programming in the real world isn't a popularity contest.
This is a very large cope. Everything humans do from deciding what to eat, to deciding who gets promoted at their job, to deciding how to run a democratic country is a popularity contest.

Being told things aren't popularity contests, and worse behaving as though that is true, is a form of Slave Morality. It is useful to people who are currently powerful for you to believe it, because it will divert you and a lot of other people into tasks which do not challenge that popularity/power.
>>
>>15005495
I wish my refrigerator was that explicit. Thanks.
> You could try putting a thermometer in and then switch it to the extremes and see.
Lmao.
>>15005187
If you write $X_{1 - 2}$ people will just interpret that as $X_{-1}$
>>15005188
>which is easier and less time-consuming for an absolute beginner. I don't have a lot of spare time.
Give up on C++. Time sink language.
>>15005631
>There is a reason no other language has made it into the Linux Kernel since it was first written until Rust.
That being because Torvalds was filtered by C++.
C++ provides numerous security advantages over C when used at least somewhat idiomatically and with cautious implementations of things like vectors (overloading the [] operator to do bounds checking takes basically no effort). It's not as safe as Rust, but it's much better than having to count mallocs and frees.
>>15005650
>There are no real advantages to using it over C currently
That's plainly false.
Rust has a tremendous advantage over C and C++ called "a baked in build system".
>>
>>15004641
How do I stop lovin le heckin sciencerino?
>>
If I have $\lim_{x\to +\infty}$ of some expression, can I w.l.o.g. assume $x>1$?
>>
>>15005689
Yes.
>>
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When finding the area between two curves what determines what the top and what the bottom function is
>>
>>15005689
yes, you can pick any other constant too
>>15005652
https://www.kenteklaserstore.com/products/laser-beam-evaluation/view-it-ir-infrared-laser-beam-detectors
idk something like this? material spec just says "aluminum", I'm not sure what the transparent material in these is but they're not that expensive
be aware this only converts 800-1700 nm IR though
>>
>>15005825
whichever function is bigger in that region, for 0 < x < 1, x^1/2 > x^2 always
if they cross you need to split the integral at the intersection and switch the signs depending on which is bigger
>>
>>15005830
thx
>>
>>15005825
Integral shows the area of between the curve and x axis.
Area is negative depending on whether function is negative.
>>
For any chem guys in here.
>You are making a buffer solution and the initial pH is 8.3. You need the final pH to be
7.4. What would you add to the solution to adjust the pH to the final value?
They don't give you pKA. They don't give you concentrations. The don't give you names of what you're working with. They give you absolutely nothing except this. So barebones and so devoid of any substance that it feels like it sets you up to be wrong. What the fuck do you do to solve this? Is it a question where the answer is stupid simple and basic, but we are conditioned to try to use Henderson-Hasselbach to solve buffer equations? I don't understand
>>
>>15005825
doesn't matter. Just take the absolute value if you end up getting a negative value
>>
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I get how he gets f ' and how he gets f, but what are f(0) =3 and f(1) =2 supposed to do I dont really understand anything after he gets the second antiderivative.
>>
>>15005914
since you integrate the function twice you have two constants, those two conditions allow you to deduce the values of said constants (just substitute $x$ with 0 and 1 and solve for $c_1,c_2$)
[eqn]f(x) = \frac{x^5}{4} + \frac{x^4}{2} + x^2 + c_1 x + c_2 \\
f(0) = 3 \implies c_2 = 3 \\
f(1) = -2 \implies c_1 + \frac{19}{4} = -2 \implies c_1 = -\frac{27}{4}[/eqn]
>>
If I have a data set normalized to a max value (e.g. max = 200 so 0.5 = 100), and I take the standard deviation of this, does it fuck up my units/normalization? Or can the stdev be interpreted the same way as the original data set?
>>
>>15005882
dilute with water?
t. clueless physicist
>>
>>15005949
The standard deviation has the same unit of measurement as your original dataset: look at the formula and you'll see that if you multiply (or divide) every data point $x_i$ by a constant $C>0$, then the standard deviation also gets multiplied by $C$.
>>
>>15005973
That's what I thought, thanks anon.
>>
>>15005949
You can use coefficient of variation, to get a measurement of variation that is invariant of what units you are using.
>>
>>15005678
C++ (and many other languages) have garbage collection. You can't have g.c. in a kernel. That fact Rust avoids that while also having all those security features and bounds checking is one of the reasons it was chosen.
>>
>>15006078
>C++ (and many other languages) have garbage collection.
It doesn't.
You should be thankful this is an anonymous imageboard, because after that one I'd just ignore literally everything you could possibly say about C, C++ or Rust.
>>
>>15006097
Weird. In my head I meant Go but my fingers wrote C++.

But saying that C++ does have it's own issues that makes kernel development in it problematic.
>>
>>15006109
>But saying that C++ does have it's own issues that makes kernel development in it problematic.
Name one issue that doesn't apply to either C or Rust.
>>
some very good wemis in here
>>
if i know positions of two points of a triangle and length of all sides then the third point of the triangle can only be in two possible positions is that correct?
>>
>>15006139
four
>>
>>15006142
This, unless the other two lengths are equal.
>>
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>>15006142
how can that be possible? if the X points are fixed
and i know all lengths like ab, bc, ca
how can it be more than two possible positions for the third point?
>>
>>15006148
oh, by "length of all sides" i didnt realize you meant specifically which sides had which length. two then.
>>
will I be single forever?
>>
>>15006173
maybe. up to you.
>>
>>15006150
okay one more question, same situation but i have 3 points with known locations and i know lengths of all 4 individual sides, how many possible positions for the 4th point?
It should be just one right?
>>
>>15006115
C++ leads to really really bad design choices. You invariably start using the "nice" library features of the language like STL and Boost and other total and utter crap, that may "help" you program, but causes:

- infinite amounts of pain when they don't work (and anybody who tells me that STL and especially Boost are stable and portable is just so full of BS that it's not even funny)
- inefficient abstracted programming models where two years down the road you notice that some abstraction wasn't very efficient, but now all your code depends on all the nice object models around it, and you cannot fix it without rewriting your app.
- the whole C++ exception handling thing is fundamentally broken. It's _especially_ broken for kernels.
- any compiler or language that likes to hide things like memory allocations behind your back just isn't a good choice for a kernel.
- you can write object-oriented code (useful for filesystems etc) in C, _without_ the crap that is C++.
>>
>>15006210
No shit.

>muh portability

>any compiler or language that likes to hide things like memory allocations behind your back just isn't a good choice for a kernel.
I literally just said issues that don't apply to either C or Rust.

Exceptions barely cut it but you can just not fucking use them.
Also, and this is important to mention, exceptions mean that you can catch things like bad allocs when manipulating data structures in C++. If a rust program runs out of memory it will die, instantly, and if this is the kernel, your computer just fucking crashed.

>inefficient abstracted programming models where two years down the road you notice that some abstraction wasn't very efficient, but now all your code depends on all the nice object models around it, and you cannot fix it without rewriting your app.
It's almost as if this applies to any programming language in the world.
>>
Anyone else buys new books because they're too socially awkward to buy used ones?
>>
is there any reason why matrix multiplication is so faggy?
addition is super simple, you just add corresponding positions, but with mutiplication you have to like do whole rows and shit, why?
>>
>>15006378
>>
>>15006378
A matrix represents a function. Matrix multiplication is function composition.

y1 = a.x1+b.x2
y2 = c.x1+d.x2

z1 = e.y1+f.y2
z2 = g.y1+h.y2
=>
z1 = e.(a.x1+b.x2)+f.(c.x1+d.x2) = (ae+cf).x1+(be+df).x2
z2 = g.(a.x1+b.x2)+h.(c.x1+d.x2) = (ag+ch).x1+(bg+dh).x2

[eqn]
\begin{pmatrix}e & f \\ g & h \end{pmatrix} \begin{pmatrix}a & b \\ c & d\end{pmatrix} = \begin{pmatrix}ae+cf & be+df \\ ag+ch & bg+dh\end{pmatrix}
[/eqn]
>>
>>15006192
this is the exact same question. its still two.
>>
>>15006480
shieeet i wish i paid more attention in school, i had no idea i would be needing to use this shit in actual real life decade later
>>
>>15006505
what are you even doing?
>>
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>>15006510
laser cutting
i have 3 "homing" points of which i know the position before and after, and a bunch of other points for the laser to cut of which i only know the before positions, so when i move the material with the points on it, and find out the new x,y positions of the homing points, i then can use this triangle shit to re-calculate the positions of all the other points (tens of thousands of them), since they are always in the same position relative to the homing points.
I tried to do it with 2 homing points but it doesn't work because the stupid triangle can be drawn mirrored too, but with 3 homing points i can make two triangles, each will produce two sets of coordinates for each triangle (two possible position where the point i'm recalculating can be), but i can simply check which of the two sets of coordinates are identical (common corner between both triangles), and it will tell me that is the new coordinate i need.

See pic, i use 3 of the homing points to draw two triangles where the point i want to calculate is the common corner, which helps me to eliminate the wrong pair of coordinates which the quadratic equation returns to me.
Pretty fucking smart if i do say so myself, i am pretty proud of this solution i came up with specially because i didn't do any math since high school
>>
>>15006550
i fucked up the drawing, the dotted lines were supposed to show where the alternative triangles could be drawn, since the blue point can be in two positions, but you get the idea
>>
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>>15006115
>>15006097
>>15006132
>>
>>15006550
im happy that youre proud of your solution anon. if youre not completely flipping the material over, and if whatever system youre using can differentiate between all the homing points, the way that i would solve this is to just have two homing points (or more, for redundancy) and use their befores and afters to solve
[eqn]
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
\begin{bmatrix}
x_i \\
y_i
\end{bmatrix}
=
\begin{bmatrix}
x_f \\
y_f
\end{bmatrix}
[/eqn]
>>
>>15006597
or actually, you need a 3d matrix for translations
heres some reading material if youre interested https://web.cse.ohio-state.edu/~shen.94/681/Site/Slides_files/transformation_review.pdf
>>
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>>15006597
>if youre not completely flipping the material over
i am, i am turning it over to laser the second side, that is the reason why the material gets moved
but i am thinking this will simply be solved by mirroring the the homing points on their center x axis

> and if whatever system youre using can differentiate between all the homing points,
i am the system here, i manually measure the positions of the homing points and input them into the program i'm making that recalculates the gcode positions
thanks for the link, but that is bit too advanced for me. the language i am writing this in has functions for doing math with matrices (multiplications etc), but i have no idea how to fill in some of the variables needed, for example there are matrices that have cos(θ) in them.. what am i supposed to fill in for theta there? angle theta of what? Rest of it i could probably figure out.
>>
Is the following claim true?
[eqn]\lim_{x \rightarrow \infty} f \left( g(x) + h(x) \right) = \lim_{x \rightarrow \infty} f \left( g(x) + \lim_{x \rightarrow \infty} h(x) \right) [/eqn]
For example. Is this a valid step in finding a limit?
[eqn]\lim_{x \rightarrow \infty} f \left( x + 1/x \right) = \lim_{x \rightarrow \infty} f \left( x + 0 \right) [/eqn]
>>
>>14996226
If you can't do the first one, you didn't read the book. For the second you can start by using Adam's law, conditioning on $B_s$. For Q2, use the idea that $B_{2T} = B_{2T} - B_T + B_T$ and integrate.
>>14996769
You can write them as factorial ratios and use results from here https://arxiv.org/abs/0709.1977
>>14997858
>>14997898
The main idea is fine, good job. You could be a little more clear (I want to prove the the l.u.b. of the sequence st ... is 1 / why does such a c exist (your sequence is increasing) / ...)
>>
>>15006660
If $f$ is discontinuous it is clearly false. Take for instance $f(x) = 1_{\{x>1\}}, g(x) = 1, h(x) = \frac1x$.
If $f$ is continuous you can take the limit inside', but that's not exactly what you want. In general, your claim is false; you can note that $x+ \frac1x$ is increasing to find your limit.
>>15005117
>>15005633
>>
>liked math in highschool
>ended up going for a cs bachelors
>like math classes and algorithms the most
>sure at this point that I don't want to work as a commercial programmer long term
is there anything I could pursue that's between cs and math?
I would probably like puruing math but it seems like that ship has already sailed
>>
>>15006723
Operations research / optimization? There's plenty of work in it. Here is a (random) site with some details: https://www.cwi.nl/research/groups/networks-and-optimization
>>
>>15006643
>i am, i am turning it over to laser the second side, that is the reason why the material gets moved
ah, i see. then you can do the matrix stuff with three points (or even two, you would just have the tell the system whenever you flip it over)
>that is bit too advanced for me
not at all, its just multiplication and addition, but written in a fancy way.
lets say you have two points $A$ and $B$ that start at $A_0$ and $B_0$ and end up at $A_1$ and $B_1$. you start by flipping everything over the x or y axis (theyre equivalent by 180 degrees). then, you slide $A$ over to $A_1$. then, you rotate everything around $A_1$ until $B$ lines up with $B_1$. simple. in practice, since matrix rotations are only around the origin, you have to do things in a special order:
1. flip if necessary
2. subtract $A_0$ from all points
3. rotate all points by $\theta$
4. add $A_1$ to all points
each step is its own matrix. matrices 1, 2, and 4 are easy. finding $\theta$, like you said, is a bit tricky, but its just some trigonometry. the angle that a vector makes with the x axis is
$\displaystyle \theta = \arccos \left( \frac{x}{\sqrt{x^2 + y^2}} \right)$
so, subtract $A_0$ from $B_0$, subtract $A_1$ from $B_1$, find the angle of both, and subtract the two.
$\displaystyle \theta = \theta_{B_1-A_1} - \theta_{B_0 - A_0}$
i know this looks hard but if youre actually transforming tens of thousands of lines, this is WAY better than solving a quadratic. once you have all four matrices, you just multiply them together to get your final transformation, and you can just use that matrix on each point (computers are pretty good at matrix multiplication).
final pitfall: you need to multiply matrices in the reverse order that theyre supposed to be applied.
>>
>>15006734
alright, thanks i'll look it over
>>
>>15006733
seems great. will look into it more in depth
thanks, mate
>>
>>15006751
here if you need me
>>
>>15006755
Extremely cute post.
>>
i dont understand what it means that the scalar product is bilinear
>>
>>15006814
The map
[eqn] V^2 \to \mathbb{R} \\
(x,y) \mapsto \langle x,y \rangle[/eqn]
being bilinear means that for each $a,b \in V$ the maps
[eqn] V \to \mathbb{R} \\
x \mapsto \langle x,b \rangle[/eqn]
and
[eqn] V \to \mathbb{R} \\
y \mapsto \langle a,y \rangle[/eqn]
are linear maps.
>>
>>15006814
Linear map
$f(x+y) = f(x) + f(y)$
$f(ax) = af(x)$

Bilinear map
$f(x + y,z) = f(x,z) + f(y,z)$
$f(x,y+z) = f(x,y) + f(x,z)$
$f(ax,y) = af(x,y)$
$f(x,ay) = af(x,y)$
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>>15006821
>what exactly is magnetic flux?
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>>15006821
>>15006827
thank you guys :)
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Why is the highlighted part true?
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is there some sort of correlation between learning and depression, or learning, depression, and autism? Every time I go through a depressive stage learning just gets easier. Topics that fucked up my head became more understandable for some reason after I go through mental dips
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>>15006734
welp, i guess i am just too brainlet to figure it out after all, if you feel like it could you please show me an example how would the equation with the matrices look like? because i keep getting nonsense, that should be last spoon feed i need hopefully
so to make clear exactly what is happening movement wise:
let's say if i want to use two homing points, and then have a third point for which i want to calculate the new position.
We start with knowing positions of all 3 points, let's say 1,2 3,4 for the homing points and 4,2 for the extra point
then i flip the whole thing on x axis by exactly 180 degrees (i turn the material over in the laser cutter).
But because i am turning it by hand, it will end up in slightly different (unknown) position and also have a bit of (unknown) rotation on z axis
In the image, let's say the blue square is the bed of the laser cutter, that never moves, and it is the basis of the x,y coordinate system in which the points are located.
Now through through some camera magic i will find the new coordinates of the two homing points, for simplicity let's say 2,4 and 4,2 (so here the rotation on Z axis is 0 but in real world there will always be some)
So how would i calculate the new coordinates of the extra point which was originally at 4,2?

I promise this is the last time i'm asking, but if you don't feel like doing it, it's totally fine.
>>
can literally only handle 2-3 pages at most of math text a day self study. am i going to make it?
>>
>>15007503
Let Y = {a,b}. Every neighboorhood of (n,a) contains (n,b) and every neighboorhood of (n,b) contains (n,a).
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>>15007503
Let $x=(n,y)\in A\subset X=\mathbb{Z}\times Y$. Then let $(n,y')\in X$ for some $y'\neq y$.
Note that all basis elements containing $(n,y')$ are of the form $B_{y'}=(a,b)\times Y$ due to the trivial topology on Y and where (a,b) is some integer interval containing n.
Hence, $(n,y)\in B_{y'}$, so that for all open sets containing $(n,y')$ the intersection with subset A of X is nonempty i.e (n,y') is a limit point of A.
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>>15007941
Depends on the text. I understand if you are doing something like differential geometry. But with something like linear algebra idk man you been seeming kinda sus lately.
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>>15007959
aluffis algebra chapter 0
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>>15007941
>am i going to make it?
doesn't really matter, AI robot waifus are coming within a decade and will do all the math for us, meatbags won't be able to compete
>>
Though I understand that we're calculating the orientation after rotation, wouldn't that mean we'd have to use a greater vertical distance than 300mm?
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>>15007981
In that case you cant even assume a right triangle anymore right? I think we just assume the small angles doesnt change the lenghts that much?
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>>15004641
For undergrad level math how many hours a week on average will I have to study?
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>>15007994
Yeah, that was the issue I had with it. Ah maybe so, since the chapter implies we're measuring for very small amounts of strain that would make a lot of sense actually. Thanks for clearing that up.
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>>15007941
Make it where? Get a tenured professorship?
I doubt it, but I'm not going to say that you absolutely cannot con your way into one.
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>>15007941
how many hours a day?
Also, depends on the density of concepts.

>>15008005
Depends on your IQ. Some guy studying 15 hours a week absolutely mogs another midwit studying 40 hours a week.
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>>15008113
>IQ
IQ is a pseudoscience
>>
>>15008113
I got tested 133 IQ what would you guess I'll have to study?
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>>15008196
23 hours and 42 minutes per week.
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>>15008196
you need to study how IQ is irrelevant
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>>15007936
sorry, was sleeping
>I promise this is the last time i'm asking, but if you don't feel like doing it, it's totally fine.
we're here to help, anon.
do you understand what i said about sliding the first homing point over, and then rotating about that point to line up all the other points? do you understand why those 4 matrices i listed would accomplish that?
lets go through an example. you can find the formulas for all these matrices in that pdf i linked.
>1. flip if necessary
$\displaystyle M_1 = \begin{bmatrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$
>2. subtract A_0 from all points (1,2)
$\displaystyle M_2 = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & -2 \\ 0 & 0 & 1 \end{bmatrix}$
notice that we're adding the x coordinate here, instead of subtracting, because we just flipped A_0 and B_0 over the x axis.
>3. rotate all points by θ (remember that the x coordinates of A_0 and B_0 here are flipped)
$\displaystyle B_1-A_1=(4-2,2-4)=(2,-2) \\ \theta_{B_1-A_1}=\arccos \left( \frac{x}{\sqrt{x^2+y^2}} \right) = \arccos \left( \frac{2}{\sqrt{2^2+(-2)^2}} \right)=0.785398... \\ B_0-A_0=(-3+1,4-2)=(-2,2) \\ \theta_{B_0-A_0}=\arccos \left( \frac{-2}{\sqrt{(-2)^2+2^2}} \right)=2.35619... \\ \theta=\theta_{B_1-A_1}-\theta_{B_0-A_0}=-1.57079... \\ M_3 = \begin{bmatrix} \cos(\theta) & \sin(\theta) & 0 \\ -\sin(\theta) & \cos(\theta) & 0 \\ 0 & 0 & 1 \end{bmatrix} = \begin{bmatrix} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}$
notice that we actually did get rotation; the angle of the starting and ending points are the same, but once you flip over the x axis you have to rotate to get it lined back up.
>4. add A1 to all points
$\displaystyle M_4 = \begin{bmatrix} 1 & 0 & 2 \\ 0 & 1 & 4 \\ 0 & 0 & 1 \end{bmatrix}$

cont.
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>>15007936
final transformation:
$\displaystyle M = M_1 M_2 M_3 M_4 = \begin{bmatrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & -2 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 1 & 4 \\ 0 & 0 & 1 \end{bmatrix} = \begin{bmatrix} 0 & -1 & 4 \\ -1 & 0 & 5 \\ 0 & 0 & 1 \end{bmatrix}$
now, if you wanted to find the point that (2,5) maps to, you just do
$\displaystyle \begin{bmatrix} 0 & -1 & 4 \\ -1 & 0 & 5 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 2 \\ 5 \\ 1 \end{bmatrix} = \begin{bmatrix} 8 \\ 2 \\ 1 \end{bmatrix}$
and see it maps to (8,2).
that pdf says you do the multiplication left to right, so i went with that, but im pretty sure i read that it was right to left in order of application, you might want to try both, or consult the manual of whatever language youre using.
heres a link to visualize whats happening https://ncase.me/matrix/.
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>>15008299
whoops, i changed the order of the matrices without changing the result. actual final transformation left as an exercise.
>>
Why is gay lisp a thing?
>>
>>15008391
alcohol during pregnancy causes cleft lip and homosexuality
>>
I dont understand how there can exist an oracle B such that relative to B, P is not NP. We don't know whether P is NP or not in general. An oracle B just lets a Turing machine quickly decide some language. So an oracle can only possibly make problems easier. So the existence of B means that if a Turing machine has help, we know there are some NP problems that it can't solve in polynomial time. Surely, without the help of an oracle, those same problems are not going to become solvable in polynomial time, right? If a Turing machine can't solve an NP problem in polynomial time with help, then that means it can't solve that problem in polynomial time without help either. But I know I must be wrong since we don't know whether P is NP or not.
>>
>>15004641
Hey anons, I'm currently in EE and studying control theory. I recent bought ELEGOO Smart Robot Car Kit V4 to play around with. In class, I used raspberry pi, but kit is arduino. Is there any guide or reading to implement a simple PID to do matching pursuit? I do have a bit of knowledge on embedded, like scheduling with RTOS. Any suggestions would help. Thank you.
>>
>>15008445
post whatever specific passage you're confused about, it's impossible to help you understand the usage of an oracle without knowing how the oracle is actually used in detail
>>
Let $\mathcal{A}$ be an algebra of sets on $X$. When is it useful to replace the inclusion $X\in\mathcal{A}$ by the existence of the unit of the algebra $E\in\mathcal{A}$ (a set such that $A\cap E = A$, for all $A\in\mathcal{A}$)?
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>>15008677
What definition of algebra of sets are you using?
In my understanding algebras of sets need to be closed under complements, so they all contain $X$.
>>
Is there a number p such that $\{q \in \mathbb{q}, q < p\} = \{q \in \mathbb{q}, q \leq 1\}$?
I want to say no but I'm not sure. Intuition tells me that you can always find a number closer to 1.
Also, how does this hold for the real numbers?
>>
>>15008775
is $\mathbb{q}$ supposed to be the rationals? if so then your intuition is correct. something something $(1, \infty)$ doesnt contain its own infimum, iunno remi can probably explain better.
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>>15008743
the book I'm reading defines it as a class of subsets of some fixed set $X$, such that $\emptyset, X\in\mathcal{A}$ and if $A,B\in\mathcal{A}$, then $A\cap B, A\cup B, A\setminus B \in\mathcal{A}$. It then notes that $X\in\mathcal{A}$ can be replaced by the wider assumption of the existence of the unit of the algebra. I don't understand when this is useful.
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>>15008792
Yes, I meant $\mathbb{Q}$.
It kind of makes sense intuitively but it'd also be weird. Doesn't that mean that a family of sets containing all open intervals intersected with a set containing all closed intervals form the empty set?
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>>15008818
not at all
$(0,1) \cap [0,1] = (0,1)$
$[0,1) \cap [1,2] = \{\}$
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>>15008825
Family of sets, so consider a set containing all open intervals like $\{(1,2),(1,3),(1,4)...\} \cap \{(1,2],(1,3]...\}$
>>
what's so spectral about the spectral theorem (why is it called like that)
>>
>>15009065
The spectrum of a linear map $T$ are those values of lambda such that $T - \lambda$ has no continuous inverse.
The spectral theorem is about decomposing $T$ into parts on which the linear map is as simple as possible. If the spectrum is finite then you can write $T = \sum_{k=1}^n \lambda_k P_k$ where the $\lambda_k$ are exactly the elements of the spectrum and the $P_k$ are projections into disjoint spaces belonging to each spectral value.
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>>15008842
Not the same anon, but a family of sets can be finite, and for you're question it wont matter whether the family is actually finite or not. Anyway, to answer your question, if you're talking about an intersection of sets like the example you've given, then yes it will always be empty, because none of the elements are actually the same. Even if intervals (x, y) and (x, y] overlap, as elements of a family of sets, they're distinct. For example, { (x, y), (x, y] } contains two distinct elements. More generally, sets A and B are equal if and only if they contain all the same elements, i.e. if for all elements x, x is in A iff x is in B. If our sets A, B are intervals with A=(x, y) and B=(x, y], then B contains an element which is not contained in A, namely y. Hence A and B are distinct sets, and if we take the intersection of {A} and {B}, it will be empty. Note that if we take the intersection of A and B, however, it will not be empty, it will be equal to A. The intersection of {A} and {B} is completely different from the intersection of A and B because a set A is a completely different set from the set {A}.
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>>15004641
Does $\{\O} \subseteq \O[\math] >> >>15009117 [math]\{\emptyset\} \subset \emptyset$
fuck
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>>15008816
>>15008816
It's useful in probability and real analysis. In probability, they like to make use of an algebra of sets, because the look at "events", which are basically just sets which are thought of as representing collections of possible outcomes, and the if event X and event Y, then we want the events X u Y (X or Y) and X n Y (X and Y) to be well defined, and hence we want a collection of sets representing these events to be an algebra of sets, i.e. we want it to satisfy the properties you mentioned. The other property, closer under complements is also useful in probability, of course, and in that case it means something like the event where A occurs and B does not occur.
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>>15009117
That would be incorrect as you've written it, but if you reverse the positions of {0} and 0 it's correct. What does it actually say? Well keep in mind that any set, even the empty set 0 is itself an object, and like any other object it can appear as an element of a set. In this particular case, the empty set 0 is itself an element of the set {0}.
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>>15009139
im still a bit confused. i understand that $\{\emptyset\}$ is an element as any other and that it doesnt seem to be contained in the empty set itself.
but if $\{ X \} \subset Y$ then $X \in Y$, right? the other way around also seems to make sense (idk if this is valid)

so, if $\emptyset \in \emptyset$ then $\{ \emptyset \} \subset \emptyset$

what am i doing wrong
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>>15009158
the empty set is not an element of itself, since it (by definition) has no elements
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I don't know how to do these problems. I only know that I have to show the chemical reactions, find out the mole for every compound and then do what's asked in the question.
>>
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>>15004641
I've read that Ph.D engineers from 50 years ago say modern undergrad curriculum is as difficult as their doctorate work. Is that true? Total BS? A mix of truth where modern standards of understanding and competence are noticeably higher than in the past?
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>>15009102
Yes, the question is whether there exists a set with an open interval equal to a set with a closed interval.
My conjecture is that there's no such thing.
Proof: Consider a set $( \infty , 1]$. Take the equivalent set $\{ x \in \mathbb{R} : x \le 1\}$ and a set $B = \{x \in \mathbb{R} : x < p\}$
Then for any $p > 1$ there exists the number $\frac{1 + p}{2}$ which is always $1 < \frac{1 + p}{2} < p$ because $2 < 1 + p < 2p \iff 1 < p < 2p - 1$ and therefore the set $B$ contains at least $A \cup \{ \frac{1 + p}{2} \}$.
For cases $p \le 1$, then $B \subseteq A \setminus \{p\}$.
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>>15009542
The inverse is true.
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>>15008299
thank you, i think it's clear enough now for me where i can see what is going on
i should have no troubles using it
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>>15009131
Thank you, that makes a lot of sense. I still don't quite understand when it's useful to replace the condition $X\in\mathcal{A}$ with the wider assumption of the existence of the unit of the algebra $E\in\mathcal{A}$ with the property $A\cap E$, for all $A\in\mathcal{A}$.
>>
>>15010011
>>15009131
*with the property $A\cap E=A$
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>>15009523
>I only know that I have to show the chemical reactions, find out the mole for every compound and then do what's asked in the question
>I don't know how to do these problems
wtf??? That is all you have to do!!! look up/calculate the molar mass of Urea divide 1000 by that, use the amount of moles of oxygen and hydrogen is used in the reaction and use proportionality to calculate the resulting mass. This is literally highschool shit! I don't even study chem
>>
Holy shit I just realized I forgot to intergrate after replacing u on my calc test. He hasn't posted the grades yet. I'm gonna fail fuck fuck fuck
>>
why do nuclear fuel rods have a life time limit again? Isn't uranium magnetic and could thus be kept confined in a magnetic field while heating water?
>>
Do physics work differently based on scale? We spend like half an hour arguing about this with friend the other day.
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>>15010118
yeah, that's the reason we use Einstein's general theory while studying cosmic objects, Newton's laws at small scales and quantum mechanics at sub-atomic level.
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>>15010118
Of course not. The laws of physics are universal and apply everywhere and in all situations. However the effects of those laws may differ depending on scale.
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>>15010122
>>15010134
well thanks a lot
>>
Why does ftl communication violate causality?
>>
let's say i have i have 2 points in 2d space

x1,y1 and x2,y2

the two points lay on a line and i want to move the second point to be exactly N distance away from the first point, in a way where they are still sitting on that same line, how can i calculate this?
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>>15010185
Call the given points $p$ and $q$. Then the point you want is
[eqn]p + N\frac{q - p}{\|q - p\|}[/eqn]
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>>15010195
thanks, just one question what operation does this denote? ∥
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>>15010199
Norm.
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>>15010151
You could receive a message before someone sent it.

>>15010185
Calculate the unit vector between the two points $\hat{v} = v / |v|$ then add $N \times \hat{v}$ to the first point.
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>>15010201
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>>15010199
It's the length of vector. There are many different ways to define lengths in $\mathbb{R}^2$.
The simpelest ones would be the $L^1$ norm
[eqn]\left\| \begin{pmatrix} x \\ y \end{pmatrix} \right\|_{L^1} = |x| + |y|[/eqn]
or the $L^\infty$ norm
[eqn]\left\| \begin{pmatrix} x \\ y \end{pmatrix} \right\|_{L^\infty} = \max(|x|,|y|)[/eqn]
No norm is any more or less correct than another one.
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>>15010214
i see so

say ∥[-3,5]∥ is simply = 9?
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>>15010260
shit, i meant 8
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>>15010263
wait i just tried it on wolfram and each norm type gives different result, so i used the norm 1 for my calculation and it seems correct but if i used another form like 2 it would not work since that would be 5.8... kinda confusing
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>>15010276
That's because your original question was not precise. What norm do you use when you mean N distance''? (probably the 2-norm).
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>>15010204
How would you receive the message before someone sent it rather than the same moment it was sent?
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>>15010277
well, if you have numbered x axis
1,2,3,4,5 and so on,
and the distance between 1 and 2 is 1cm, (2 and 3 is also 1cm and so on) (so the whole thing is drawn on a 1cm grid)
then if i say distance of 2 i mean 2cm between point 1 and point 2
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>>15010214
>>15010277
is this fun for you?
>>15010199
its the magnitude of the vector, aka length. use the pythagorean theoreom. $\sqrt{x^2+y^2}$.
>>
$a,b,x,y \in \mathbb{Z} \\ (a^2 + b^2)^n = x^2 + y^2$
How do I prove this? It's an exercise in the complex number section of this book but I don't even know how to approach it.
>>
>>15010294
It's an open problem.
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>>15010294
prove what? that such an n always exists?
use phasors.
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>>15010298
No, that such an x and y exists for all $n \geq 1$. I don't know what a phasor is
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>>15010289
>is this fun for you?
I am not the same guy
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>>15010302
wait i cant fuckin read, nvm what a phasor is.
iunno bro >>15010297 says its open so.
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>>15010297
It doesn't seem like an open problem. Any evidence for this claim?
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>>15010307
both of those posts were pretending like they didnt know what "distance" was.
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>>15010294
It's false for a = b = x = y = n = 2
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>>15010320
I said he probably means the 2-norm though. Clearly he could calculate any as he gave examples of multiple calculations he had done. I also explained why he was confused by the other guy being so dense as to mention any norm is fine.
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>>15010294
[eqn](a^2 + b^2)^n = |a + i b|^{2n} = \left| (a + ib)^{n} \right|^2 = (\Re((a + ib)^{n})^2 + (\Im((a + ib)^{n}))^2[/eqn]
>>
>>15010331
>>15010297
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>>15010327
alright, sorry, i can see you were trying to help
>>
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>>15004641
how do i identify the order of a bode plot?
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>>15010344
look up how much the magnitude increases/decreases over a decade
in your case you have a 20dB loss per decade so it's a first order
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>>15010278
Alice and Bob are on two separate spaceships.

Alice sends a message to Bob at FTL speed. Bob turns his ship and flies towards Alice at FTL, and once he arrives says "I got your message."

This doesn't have to break causality but depending on the relative velocities of the two ships there are certain configurations (like if the two ships are initially flying away from each other at a large percentage of c) then if you draw the space-time diagrams Bob arrives at Alice before she even sends the message.
>>
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>>15010344
It's hard to say unless you at least know the corner frequencies.
You can identify the type of the system by looking at the initial slope, which is -20dB/decade in your case, so it's type 1 system (1 pole at origin).
>>
>>15010331
Thank you.
>>
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Any medfags here, I am sitting here shitting myself softly wondering if I have cancer (I'm 41). I noticed a red mark on my right shin in the shower about a month ago, thought I must have bumped my leg, but didn't remember bumping it, plus the mark didn't hurt like a fresh wound would. Looked at it yesterday and realised it's actually bigger now, tenderer now, and there is a bruise forming around it. Suddenly I think I have skin cancer. I have made a doctor's appointment in 6 days, but am reading about skin cancer and wondering if I should try to see a doctor sooner.

All pictures: https://mega.nz/folder/W5VBWQqB#e7eR9cA2jUtx1VWf0mL9Lw
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>>15010611
You can click on the dots on the image and click "preview" btw to view all the images in browser.
>>
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So does $m_{B_1\; \cap B_2} = \inf_{x\in\mathcal{B} }f(x)$, where $\mathcal{B}$ is any base that contains $B_1 \cap B_2$, or is it a typo and supposed to be $m_{B_1\; \cap B_2} = \inf_{x\in B_1 \cap B_2 }f(x)$?
>>
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How would I calculate the time a spaceship needs to fly to a star or something that is 4.2 light years away, when it is at the orbit of mars going at a speed of 40km/s with only the suns gravity to pull it back.

I came to this funktion(f in picrel) but I get a number that looks too odd(c is in seconds and d is in years).
>>
If an infinite set of vectors $A$ is said to be linearly independent, does that mean every countably infinite subset of $A$ is linearly independent or just every strictly finite subset?
>>
Does squaring the amplitude of the electric field to get the intensity in electromagnetism explain Born's rule?
>>
>>15010812
Every finite set is enough.
>>
How do i prove AxB ~ BxA, where ~ is equinumerous?

I need to find a function that maps (a,b) in AxB to (c,d) in BxA? But I cant think of one
>>
>>15010967
f(a,b) = (b,a)
It's that simple.
>>
>>15005882
i think this might be just a trick question with the given values, making you assume you have to do some quantitative problem solving. i think i would probably just say that you need to add more conjugate acid to the solution or something.
>>
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>>15010611
You will die.
>>
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>>15010977
damn that's the one i'm actually trying to do but i'm not sure how to use it. here's what i did so far:

define f: AxB -> BxA, where f = {((a,b),(c,d)) in AxB x BxA | f((a,b)) = (b,a)}

also do i have to prove that f is a function? ie Dom(f) = X and if (x1, y) in f and (x2, y) in f, then x1 = x2?

i'm working on proving f is onto, so i have let (c,d) e BxA. I need to prove there is an (a,b) in AxB such that ((a,b),(c,d)) belong to f.

I have just switched the ordered pair to (d,c) e AxB, but how do i imply that ((d,c),(c,d)) belong to f?
>>
>>15010999
To prove f is a bijection it's enough to show that it has an inverse. The inverse is of course g(b,a) = (a,b)

g(f(a,b)) = g(b,a) = (a,b)
f(g(b,a)) = f(a,b) = (b,a)
>>
>>15011006
what i'm confused is for when i'm defining my own function to prove something, how do i know when i'm making unsafe assumptions about the sets A and B, like whether they are empty or disjoint and things like that.

also i don't know if i'm supposed to also prove its actually a function, rather than just to say it is.

that's interesting, i didnt know you could prove a bijection that way but it makes sense. but how do you prove it has an inverse?

is your example saying you have to define the inverse and then take its complement and show it equals the original function?

sorry i'm struggling a lot with functions
>>
>>15004641
>resurrect the mammoth
>grow petridish steaks
why tf don't you just focus on making the superior banana - "Gros Michel" - immune to Fusarium oxysporum f.sp. cubense first?
Cavendish bananas are bottom-tier! I pick locally grown apples any day oftheweek.
Another ethical lucrative project for biology would be to produce petridish cocoa powder since it is speculated to be extinct within five or so decades.
Petridish coffee is a third alternative to the macabre attempts of reproducing animal tissue in a lab!
>>
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I need help writing a science fiction story.

In the story, humanity coevolves with an aquatic based intelligent species that they are constantly at war with.

What environmental differences would be necessary to make it plausible that say Asia was instead partially underwater and occupied by a squid hybrid race.

Feel free to bend my parameters a bit
>>
>>15004641
>Troonhou tranime.
>>
Is Milk actually good in any way for your bones? I know about the bullshit marketing but when I look for a definitive answer they all seem broad just say " sorta" while the Vegan health sources obviously say no.
>>
>>15011378
no one knows. nutritional studies are pretty much impossible to carry out. the only real knowledge we have comes from studying individual substances, e.g. vitamin B12. so i would suggest breaking up your research into "is calcium good for you" and "does milk have calcium in it", but even then you have to take it with a grain of salt. your body is very complicated, and theres a lot of steps involved in consuming something that we know very little about.
>>
>>15011378
Calcium deficiency will cause issues with bones. If you aren't calcium-deficient, there's no benefit to having more calcium. Leafy green vegetables (cabbage, kale, broccoli) have a higher calcium content (by mass) than milk, but lower than cheese (which is basically dehydrated milk). Almonds, hazelnuts and sesame seeds are also quite high in calcium.
>>
Why do scientists make analogies while explaining things when they clearly suck at them? Just give the big boy explanation, it'd be much clearer,
>>
>>15011411
analogies sometimes suck, but youre suckin the glass dick if you think big boy explanations are clearer to laymen.
>>
>>15011411
> Just give the big boy explanation, it'd be much clearer,
No it wouldn't.
>>
>>15009523
>>15010028
And what do I do in the second question? There was supposed to be a chemical formula for oxidation of hydrocarbons but I'm not sure how to use it here. Sorry, I suck at chemistry, I never liked it, and I still have to take it as a Gen. Ed. requirement here.
>>
>>15011411
>Just give the big boy explanation, it'd be much clearer
you can't do this when 99% of laymen are fucking retards.
Try explaining to a normie what an electric field is.
Or angular momentum.
Or any other basic stuff.
And this is just the basic bitch stuff, from 200 years ago.
>>
>>15011539
>Try explaining to a normie what an electric field is.
I'm pretty sure even normalfags can an area where there is influence of electric charge is.
>>
>>15011546
what?
>>
>>15011547
Isn't that the technical explanation of electric field? Even normies can understand that.
>>
>>15011558
>I'm pretty sure even normalfags can an area where there is influence of electric charge is.
is weird, can you add some commas or something?
>>
>>15011558
But no one can understand what you wrote. ESL or dyslexic?
>>
>>15011583
ESL and I was sleepy when I wrote it sorry
>>
>>15011343
>What environmental differences would be necessary to make it plausible that Asia was partially underwater and occupied by squids
literally no changes are needed. you could replace a desert with squidlandia, imply it's pretty warm but the squids can go deeper to stay cool and have slightly better resistance than normal squids. go nuts
>>
>>15004641
Who paid you to grab Dr. Pavel ?
>>
>>15010611
looks like a regular bruise to me bro
but honestly man my arm could fall off and i wouldn't worry about it, they probably grow back
>>
if mass doesn;t affect the rate at which you fall does it least affect the rate at which you sink
>>
>>15011014
let f:A->B be a function, then a function g:B->A is a left inverse of f if g(f(x)) = x for all x in A, such a g exists if and only if f is injective. Similarly g is called a right inverse if f(g(y)) = y for all y in B, a right inverse exists if and only if a function is surjective. If g is both a left and a right inverse of f, we say g is the inverse of f and call f invertible, it follows that a function is invertible if and only if it's bijective. In the last step here >>15011006 anon showed his g is an inverse of f so f is bijective.
Proving our function is bijective in the usual way >>15010999 is just as easy
one to one: if f(a,b) = f(c,d) then (b,a)=(d,c) so b=d and a=c hence (a,b)=(c,d)
onto: if (b,a) is in BxA then clearly (a,b) is in AxB and f(a,b) = (b,a)
>also i don't know if i'm supposed to also prove its actually a function, rather than just to say it is.
sometimes you'd have to show that your function does indeed land you in the correct set and is well-defined. But in this case it's clear right? you take an element (a,b) from AxB and send it to (b,a) which is most definitely an element of BxA. This is possible for any element (a,b) of AxB, so it's a function, nothing to prove really.
>unsafe assumptions
about what? if A and B are nonempty then so is AxB and you should know this from the definition of AxB.

>>15011663
mass does affect the rate at which you fall and also the rate at which you sink
>>
>>15011676
>mass does affect the rate at which you fall and also the rate at which you sink
wtf. neither of those answers are true. stick to math.
>>
How is Langs linear algebra?
>>
>>15011663
>>15011866
Technically falling is sinking in air and the upwards acceleration created by the (negligible) buoyant force is affected by mass.
>>
I just wrote that ln(0) = 1 on an exam. I want to kill myself.
>>
>>15011890
don't just memorize formulas
>>
>>15011879
It depends on density, not mass. That's why a 1kg ball of lead sinks but a 1kg ball of wood floats.
>>
How?
>>
>>15011913
Do you know how to do it if X is fixed?
>>
>>15004641
Why do we allow chinese pedo cartoons on the internet?
>inb4 child groomers defending this shit
>>
>>15011913
Let Y be the number of Statistics majors in the sample
[eqn]P(Y=i) = \sum_{k=0}^n P(Y=i|X=k) P(X=k) = \sum_{i=0}^n \frac{{k \choose i}{n - k \choose m - i}}{n \choose m} {n \choose k} p^k (1-p)^{n-k}
[/eqn]
>>
>>15011925
last sum should also be over k; simplifying I get $\binom m i (pq)^i$, so it's binomial again, which makes sense because it's irrelevant if they say they are statistics majors before or after you sample them.
>>15011913
support is 0..m btw
>>
>>15011946
$\binom m i p^i q^{m-i}$ of course..
>>
How do I input a $T(x,o)=sin(\pi x)$ boundary condition in openFoam?
>>
>>15011899
>the upwards acceleration created by the (negligible) buoyant force is affected by mass.
Go nitpick someone else's technically correct posts.
>>
Is Algebraic Topology a dead field?
>>
>>15011879
why is it possible that statistical evidence can help infer mathematical facts?
>>
>>15011925
Why did your sum subscript change? I got this
[eqn]
P(Y=k) = \sum_{i=0}^n \frac{{i \choose k}{n - i \choose m - k}}{n \choose m} {n \choose i} p^i (1-p)^{n-i}
[/eqn]
But I suppose it's wrong since I could not simplify this to binomial.
>>
>>15011894
I have to memorize the values of a function. I was just writing shit and I think i was thinking e not ln since e^0 = 1.
The prof probably thinks I'm a complete retard (likely rightfully).
>>
>>15011971
If by technically correct you mean wrong, then sure.
>>
>>15011992
That's correct.
To simplify to binomial:
write out the coefficients and cancel what you can,
recombine them into different coefs,
consider carefully your sum index -- when are the terms zero?,
use the binomial thm.
>>
>>15012026
[eqn]
\sum_{i=0}^n \frac{{i \choose k}{n - i \choose m - k}}{n \choose m} {n \choose i} p^i (1-p)^{n-i} \\
\sum_{i=k}^n
\frac{i!}{(i-k)!k!}
\frac{(n-i)!}{(n-m-i+k)! (m-k)!}
\frac{n!}{(n-i)!i!}
\frac{(n-m)!m!}{n!}
p^i (1-p)^i \\
\sum_{i=k}^n {m \choose k} {n-m \choose i-k} p^i (1-p)^i\\
{m \choose k} \sum_{x=0}^{n-k} {n-m \choose x} p^{x+k} (1-p)^{n-x-k}\\
{m \choose k} p^{k} (1-p)^{n-k} \sum_{x=0}^{n-k} {n-m \choose x} p^{x} (1-p)^{-x}
[/eqn]
>>
>>15012096
Never mind figured it out.
>>
If $X$ and $X'$ are both finite sets with the same size, is it allowed to write
$\sum_{x \in X} P(x)$ as $\sum_{x' \in X'} P(x')$?
>>
>>15012152
if P is constant, sure
>>
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>>15011676
tyvm anon i appreciate your help
>>
They say that superfluid helium has negative friction and climbs the walls of it's container. If so, where does the energy to move the fluid against gravity come from?
>>
>>15012722
nvm I figured it out.
>>
Why would anyone take results obtained by synthetic control seriously?
The method is a complete joke.
>>
If i have that f(x) = b. how do i prove f(x) = f(x)? i feel like this will take a million steps
>>
>>15013418
What?
>>
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Why do people not talk about stem cell research anymore? Did it hit a dead end or was it just successfully prohibited in the western world?
>>
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>>15013422
i have solved in the question that f(x) = b, like for a function how you have y = f(x). but i need to show f(x) = f(x).

i've spent like 4 hours trying to figure out how to get it
>>
>>15013771
Send the question dumb ESL retard.
>>
>>15013771
so for some $x_1 \in \operatorname{dom} f$, you have shown there exists a $y_1\in\operatorname{ran} f$, such that $y_1 = f(x_1)$, and now need to show that for every $x\in\operatorname{dom} f$, there exists exactly one $y\in\operatorname{ran} f$, such that $f(x)=y$. Is this correct?
>>
>>15013787
yes i think so, sorry yes
>>
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>>15008299
So i tried making the code using this, doing it step by step as you said and it it correctly adjusts the Z axis, but it rotates over Y axis instead of X axis for the 180 degree flip. So in order to rotate over X axis, is this the only adjustment i need?
>>
>>15013828
if i adjust it like that in code it seems to correctly flip over the x axis, so it SEEMSD like thats corrent, but i want to make sure there isn't some hidden pitfall somewhere else in there
>>
>>15013826
and i also have for different question, to prove f is one to one. suppose f(x1) = f(x2), prove x1 = x2.

but i can rewrite f(x1) as (x1, y) element of f.
so (x1, y) in f = (x2, y) in f
then f is subset of XxY, so:
(x1 in X) & (y in Y) = (x2 in X) & (y in Y)

because of = now i can write (x1 in X) = (y in Y), or (x1 in X) = (x2 in X), and this no longer makes sense because this would be true for all functions. but what step did i actually break?
>>
>>15013616
It's like asking why doesn't anyone talk about heart transplants. It has gone past the hype phase into mainstream research.
>>
In stress-strain diagrams like this, how is the testing done? I've never seen negative stress & strain quantities before, only positive. Is this suppose to be a tension test? Assuming an object is being pulled apart and the forces are acting away from the specimen?
>>
>>15013832
why did you say that (x1, y) is equal to (x2, y)? This is what you're trying to prove, you can't just assume it to be true. Also please clean up your notation, you'll make fewer mistakes
>>
Why are there so many midwits here who cannot put in the effort to properly write their question yet expect someone to put in the effort to write the full answer?
>>
>>15013848
Thanks, I really didn't know what end it got after it died down on mainstream channels, I was afraid the people who complained about it had won
>>
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>>15013831
hmm i keep getting wrong positions
here is the pic with what values i am getting
1st pic is original coordinates,
second is what i'm getting after i apply the transofrmation matrix
third is what the correct values should be

it seems the transformation matrix is moving it too high on the y axis for some reason
i triple checked to make sure i am performing all the calculations as shown in the >>15008278
>>
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>>15013937
here it can be seen visualized
the correct transformation of the drawing was achieved by using the method of 3 homing points and use that to calculate two triangles. (problem is that it tranforms 99% of the points correctly but 1% them come out as nonsense, you can see it by several lines just shooting to a corner randomly in the correct drawing)

so i want to use the matrix transformation which does all points correctly, and is faster too, but there is this strange position offset
>>
>>15013959
one thing i could do to solve this, since the hardest part here is matching the Z rotation which the matrix does correctly, and only the final position is wrong, i could calculate one point using the two triangle method, then that same point using the matrix transformation and then simply see how far apart they are, and add x,y offset to all the matrix transformed coordinates so the whole thing is simply nudged into correct position, but i would really want to find out why is it in the wrong position in the first place
>>
>>15013860
looks like the convention is that positive stress and strain is extension and negative stress and strain is compression
>>
>>15013871
Shitty sketches riddled with gaps or bust.

But to answer your question, human beings are really, really bad at unconsciously estimating how much knowledge others have of things, and undergrads often underestimate how much variation there is in mathematical notation, so they ask questions here like you're their senior in college and took the same class with the same professor.
>>
What the heck is this equation? Where do I translate it? I don't think it is latex.

Computes the squared Mahalanobis distance :math:\mathbf{x}^\top\mathbf{M}^{-1}\mathbf{x}
for a factored :math:\mathbf{M} = \mathbf{L}\mathbf{L}^\top`.
>>
>>15014166
What do you mean? It is latex
>>
>>15014166
Computes the squared Mahalanobis distance $\mathbf{x}^\top\mathbf{M}^{-1}\mathbf{x}$ for a factored $\mathbf{M} = \mathbf{L}\mathbf{L}^\top.$
>>
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>>15014264
Why can't Indians shut the fuck up about Ramanujan while Mahalanobis remains unmentioned? Unlike the former's retarded le goddess spoke to me in a dream conjectures, the latter actually achieved great things.
>>
>>15013828
1. it shouldnt matter whether or not youre fliiping over the x axis or y axis.
2. youll also have to change the third (rotation) matrix if you make that edit.
>>15013959
can you mark where the origin (0,0) is in that picture? it would help in figuring out whats wrong. you can also try adjusting that rotation matrix like i mentioned above, applying each matrix one by one to see where it goes wrong, and reversing the multiplication order.
>>
>>15013959
>>15014310
also if you could mark which two points A and B youre using for the matrix calculations.
>>
>>15014327
I don't understand how matrix compositions work the way 3blue1brown shows. Yeah sure nested rotations make sense but why does $( (1,1) (-1,1) )$ squared is what it is?
>>
>Moving closer to the subject of the survey, how does one prove a statement independent of a first-order theory? There are actually two methods: consistency strength, and relative consistency. Let’s start with consistency strength. If we remove the Axiom of Infinity from ZF, we get a theory equivalent to Peano Arithmetic (PA). Now, it’s not hard to see that ZF Con (PA); that is, Con (PA) is a theorem of ZF. The reason is that in ZF, there exist infinite sets—for example, the set of all finite sets—that we can take as models for PA. On the other hand, Gödel tells us that ZF 6 Con (ZF). If we want to prove Con (ZF), we have to postulate an infinity bigger than anything definable in ZF—a so-called ‘large cardinal.’ (When set theorists say large, they mean large.) If LC asserts the existence of such a cardinal, then ZF + LC Con (ZF). So we can rank the theories in a ‘consistency strength hierarchy,’ from PA to ZF to ZF + LC. Notice that in PA, we can’t even prove that Con (PA) = Con (ZF). For then we could also prove that in ZF, and since ZF Con (PA), we’d have ZF Con (ZF), contradiction. In general, to show that a statement is unprovable in some theory, we argue that if it wasn’t, then we could collapse two levels of the consistency strength hierarchy—and thereby violate the Incompleteness Theorem.

I don't understand the last part. I get that we can show that it's unprovable in PA that the consistency of PA implies the consistency of ZF. But I don't see how that lets us show that a statement is unprovable in general. How exactly are two levels of the consistency strength hierarchy collapsed for statements in general? I can only see it working for statements that make claims about the consistency of a system higher on the consistency strength hierarchy. The author wants to say that this is an avenue for investigating whether P vs. NP is unprovable one way or the other or not. I don't see how P vs. NP could be related to the consistency of whatever system.
>>
>>15014441
>>
does anybody else miss when math books where in a portable/normal book format? Now they're all huge A4 sized and the paper used is always some shitty plastified paper
>>
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Let $G_1, G_2$ be groups and $\iota_1, \iota_2$ the canonical embeddings of $G_1, G_2$ respectively into $G_1 \times G_2$. Consider the following property: Given any two embeddings $j_1, j_2$ of $G_1, G_2$ respectively into some group $Z$, there exists a unique embedding $j$ of $G_1 \times G_2$ into $Z$ which makes the diagram commute.

Is there a name for this property?
>>
>>15014462
Fuck no. I wish fiction was in a4 size. Fuck tiny books. They are made for women with small hands.
>>
>>15014310
0,0 is top left corner of the drawing marked as original (it's where the 3 arrows are).

So i was sitting in a parking lot today thinking about how depressing and shit my life is, and then suddenly a solution came to me. I can add a 5th matrix to solve the position issue.

i can make another position matrix where
i do

M*A0 - A1

So basically i use the matrix composed from the 4 matrices to transform one of the homing points and then subtract the actual correct position of that homing point from the result
this will give me how much i have to move the drawing on the X and Y axis to be in the correct position and i tried it and it works!
So i thought i could get rid off M2 and M4 since it's the M5 that now handles the movement, but nope, if i remove them it doesn't work properly anymore. However with M1*M2*M3*M4*M5 it does
This matrix stuff is really mysterious
>>
>>15014474
Coproduct.
>>
>>15014609
Excellent, thanks
>>
By definition, two acids/bases with similar strengths shouldn't react with each other naturally right? My question is if they are in solution with another molecule that one of those acids/bases do react to, would the other acid/base interfere with the reaction?
>>
>>15013982
Ah, thanks for clearing that up.
>>
>>15013869
Aren't these equivalent notations?
$f(x_{1}) = f(x_{2}) \\ (x_{1},y) \in f = (x_{2},y) \in f$
>>
>>15014945
Depends on your encoding of functions. They're not built-in in set theory, and there are various ways to implement them. For the most standard encoding as the graph of values, that will be the case indeed.
>>
>>15015000
i'm confused though how the equality sign works in this case because you can do something like
$\\ f(x_{1}) = f(x_{2}) \\ (x_{1},y) \in f = (x_{2},y) \in f \\(x_{1},y) \in X \times Y = (x_{2},y) \in X \times Y \\ x_{1} \in X \wedge y \in Y = x_{2} \in X \wedge y \in Y \\ x_{1} \in X = x_{2} \in X \wedge y \in Y \\ x_{1} \in X = y \in Y$

I feel like it loses all meaning once i turn it into the cartesian product, but i dont see where i'm breaking any steps
>>
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Where can i find proofs of these theorems from the wiki on Equinumerosity?

https://en.wikipedia.org/wiki/Equinumerosity

I've been trying to google them but nothing is coming up probably because of the symbols
>>
>>15015147
I'm looking for proofs that use the definition of equinumerous as that there exists a function from X to Y that is bijective.
>>
What's the easiest way of finding a bunch of really easy equality math problems that are already solved?

For example a list that could contain something like
1 + 10 = 11 * 1
8 / 2 = 3 + 1
4 * 5 + 5 = 5 * 5

Or any suggestions on a code or something I can write that would do this for me?
>>
>>15014510
if i had to guess theres some bug in your code, but as long as it works it works.
>So i thought i could get rid off M2 and M4 since it's the M5 that now handles the movement, but nope, if i remove them it doesn't work properly anymore. However with M1*M2*M3*M4*M5 it does
the goal of M3 is to rotate the figure about point A, and since that rotation matrix formula is for rotations about the origin, we have to first subtract A0 from all points (the M2 matrix) so that point A is at the origin. M4 and M5 are both translations so they can be done in one step (i suspect that your M5 matrix is compensating for some error in your M4 code).
also, dont be so hard on yourself, anon. most guys wouldve stuck with your "good nuff" solution, but you decided to struggle through learning a new topic to do it the right way. that puts you ahead of 95% of people.
>>
Why so many people here complain about their exams not having questions that was done in class? Is it an American thing to expect exams just including your assignments?
>>
>>15015167
>Pick a polynomial
>Pick any point in the polynomial
>Pick any random point in the polynomial.
>Construct a new polynomial satisfying that random point.
>>
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>>15015167
try any system of equations with non-trivial solutions

>>15015575
>Why so many people here complain about their exams not having questions that was done in class?
Nobody does that; take your meds, schizo
>>
>>15015675
>>15009656
>>
>>15015167
https://mrnussbaum.com/speed-math-online-game
[spoiler]Btw silver medal.[/spoiler]
>>15015575
>take electromag class
>professor teaches us electromag
>assignments have electromag class
>go to test
>professor hands me over a clarinet and tells me to play it so he can grade my performance
Obviously there needs to be some degree of similarity between assignments and tests, but idiots sometimes expect tests to be rehashes of assignments because they've developed no understanding of the subject and cannot solve problems they haven't seen before autonomously.
>>
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>>15015309
definitely not a code bug, i doublechecked everything until my eyes bled. i'm not sure if this has effect on anything, but in my case the Y axis is reversed (instead of -1 0 1 2..., it's 2 1 0 -1..)
this is common on cnc machines. plus i also switched from y axis flip to x axis flip (>>15013828)
i'm just happy i got it to work
just for testing i tried many combinations of rearranging the matrices, or leaving some out to see what it does and one interesting effect i found that if i left position matrices, then m5 would move the whole drawing in the directiong of the z rotation instead of only on x axis (when m5 z was set to 0)
But regardless, it's working now and thats the important part, so thanks for your help fren.
>>
In what way where categories not reconcilable with Bourbaki's formalization of math?
>>
>>15015790
>in my case the Y axis is reversed
thats called a left-handed coordinate system, and i dont think theres anything right-handed specific about the math so everything should still work.
anytime <3
>>
>>15015575
when i took ODEs, there was only like 3 different power series problems that we kept repeatedly solving. the prof straight up said that one of them was gonna be on the final and it would behoove us to just memorize the solutions to all of them if we were having trouble.
>>
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Why does stupid fucking Mathchan keep saying 2019 2017 is wrong?
>>
>>15015869
Dunno but your solution seems correct to me.
Btw why are you using mathchan?
>>
>>15015884
Wait, no, I goofed.
$2 \times 2017 + 2 \times 2016 + 2016 \times 2015 = 2 \times 2017 + 2016 \times 2017 = 2018 \times 2017$
>>
>>15015869
>>15015884
It's 2018*2017.
>>
>>15015884
>>15015902
>>15015904
Well I pressed all the three similar options.
>>
How much cattle needs to be farmed to feed a single person beef everyday?
>>
Trying to solve an exercise:
Find all $n,m \in \mathbb{Z}$ such that $(1 - i)^n \cdot (1 - i\sqrt{3})^m = 32$. My thought that this should be done using the geometric form, and since 32 is real, then the sin of the argument in both numbers has to be zero, so they'd be multiples of 8 and 6 respectively. And then since you'd just multiply the absolute value of both which is $|1-i| = \sqrt{2}, |1-i\sqrt{3}| = 2$, then we get the equation $k,g \in \mathbb{Z}, 2^{8k / 2} + 2^{6g} = 2^5 \iff \frac{8k}{2} + 6g = 5$ which has no solutions (because 5 is not a multiple of 2), so there's no such numbers. Is this the correct solution? I feel like it's wrong, but I'm not sure where I made an error.
>>
will you be my bf, /sci/??
>>
>>15015956
It's clearly wrong as
[eqn](1 - i)^4(1 - i \sqrt{3})^3 = 32[/eqn]
>>
>>15015962
I will
>>
>>15015956
The error lies here
>the sin of the argument in both numbers has to be zero, so they'd be multiples of 8 and 6 respectively

The arguments tells you only that
[eqn] 3n + 4m \equiv 0 \text{ (mod 24)}[/eqn]
meanwhile the absolute values tell you that
[eqn]n + 2m = 10[/eqn]

Solving this system gives
[eqn]n = 4 - 24k \\
m = 3 + 12k
[/eqn]
for an integer $k \in \mathbb{Z}$.
>>
>>15015964
did not expect that
>>
>>15016009
:)
>>
>>15015954
It depends on how much beef the person would eat every day, and which parts of the cow they'd be willing to eat. If they'd be willing to eat cow entrails and brains, they might be able to stretch it out a bit further. If they were only willing to eat muscle meat (and only regular prime cuts), they'd get approximately 275kg of meat from a normal-sized adult cow's carcass.
A person eating one McDonald's cheeseburger, that has a 45g patty would need 16.425kg of beef over the course of one year, assuming they were to eat exactly one cheeseburger every day, which would be less than what one cow carcass would yield, but would, realistically speaking, be sourced from a variety of cows slaughtered throughout the year so as to keep the meat fresh.
A person eating 100g of beef (from arbitrarily shaped pieces of premium cuts of beef) would need 36.5kg of meat, which is still less than an entire cow, but would also most likely be sourced from many different cows, if it were meat bought at a supermarket or at a butcher shop, rather than vacuum-sealed and frozen meat from a single cow.
A person eating the entire cow carcass could get something closer to the 300-400kgs of a cow's carcass, assuming they had absolutely no problems eating entrails, brains, eyes, skin, fat and everything else a cow has.
Even though one cow should be enough to feed several people for more than a year, it only be possible if all of the meat from the cow were to be kept well sealed in a freezer at temperatures of -18C, assuming there were no power outages throughout the year, and assuming none of the people were to buy or eat any other pieces of beef available at either supermarkets or restaurants.
>>
>>15015988
>The arguments tells you only that
>3n+4m = 0 mod 24
Where does this come from?
As far as I understand, n and m have to be multiples of 4 and 3 respectively since the sin must equal 0 and the arguments are respectively $2\pi - \frac{\pi}{4}, 2\pi - \frac{\pi}{3}$. I don't see how what you said follows from this.
>>
>>15016033
[eqn]\left(-\frac{\pi}{4} \right) n + \left(-\frac{\pi}{3} \right) m \in 2 \pi \mathbb{Z} \\
-3 \pi n + - 4 \pi m \in 24 \pi \mathbb{Z} \\
3 n + 4m \in 24 \mathbb{Z}
[/eqn]
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>>15016040
Ah, okay.
As far as I understand, there are two separate conditions, $\frac{\pi}{4} \cdot n \in \pi \mathbb{Z}, \frac{\pi}{3} \cdot m \in \pi \mathbb{Z}$. Is the trick that the logical and of these conditions is equivalent to their sum, which allows you to get an equation with both? Or am I missing something?
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>>15004641
I have the option to take a math course as an elective for credit at a community college before transferring to a four year. But my options limited to Calculus 3, Intro Diff Eq or Intro Stats. My primary goal is eventually to be capable of research in AI and deep learning. But so far I've yet to take a statistics course.
I have the feeling that Calculus 3 or Diff Eq could be more valuable to me. I would have liked to be able to take both , and analysis later on, but unless I switch to math that is unlikely.

Can anyone give a recommendation?
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Does mechanical advantage rely on the conservation of angular momentum to be true?
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>>15016103
Take courses as you need them. If you encounter some course having calc 3 as a prereq, that's a good time to take calc 3. You say you want to go into AI, so just take the intro to stats course to see if you like it.
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What's the difference between gravity and magnetism?
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>>15016128
No. It relies on the conservation of energy.
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>>15016184
That's too general of a question to answer. It's like asking what's the difference between an apple and a fish. So apart from the obvious you need to be more specific.
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>>15016184
gravity acts on objects with mass, magnetism acts on charged particles
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>>15011343
Set it during the pinnacle of natural global warming, when the seas have risen and the coasts receded.
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>>15015910
It bans you for 15 minutes or so if you get it wrong.
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>>15016212
Don't all objects with mass contain charged particles - otherwise they wouldn't exist as an object?
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Does the fact that our base-10 numerical system cannot express 1/3 as a whole integer point to the fact that there is something missing?
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>>15016231
No. It's the same thing as saying base-3 can't represent 1/10
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>>15015865
yeah for some classes like diff eq or intro topology it's hard to make exam questions that are different from the exercises while still being the right difficulty
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>>15016245
Doesn't that imply base-3 is also missing something?
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>>15016279
10 and 3 are coprime, so base-10 is "missing" a factor of 3 in its radix, and base-3 is "missing" a factor of both 2 and 5 in its radix. obviously no number contains every factor, so any base you choose will have some numbers that it cant represent as finite expressions. nothing mysterious.
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>>15016279
No. You are confusing the value (1/3, 1/10, whatever) with the written representation. That value doesn't change no matter what base you use.
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>>15016225
yes
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>>15016225
>>15016291
Only if you ignore neutrons.
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LSD expires if exposed to UV, Heat, Humidity and Air.
What are the chemical processes that cause this?
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>>15016644
Just as cold reinforces chemical bonds,
so too does heat weaken them via vibration.
Like how water evaporates via vibration.
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>>15016225
Magnetism acts on moving charged particles. The direction of the force depends upon the sign of the charge. For an atom (whether moving or not), the average motion of its positively-charged particles and negatively-charged particles are equal, so the forces cancel and the average force due to magnetism is zero. Whereas gravity affects anything with mass, and the force is always attractive.
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Dumb question say I am in a real n-dimensional vector space and I have a basis that is not orthonormal but that is composed of n vectors (and therefore generates the whole vector space)

In this case what's the point of going through the hassle of applying the gram Schmidt algorithm etc to get to a orthonormal basis if I can just take the canonical n dimension basis and I know that it is 1) orthonormal and 2) generates the exact space as my starting vector?

An example in case I wasn't clear enough; in R3 I take whatever 3 vectors you want, not with a norm of 1 and not orthogonal. But they're linearly independent and therefore generate the whole 3d space. Why should I orthonormalize them if I can just take the vectors (1 0 0), (0 1 0), (0 0 1) which is also an already known orthonormal base of the space generated by my 3 starting vectors?

Maybe this question comes from the fact that my teacher just explained the theory without really telling us what's the point of all of this. Also I could ask him but I'm afraid it will make me look retarded
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>>15017789
change of basis is useful for many reasons, most notably writing linear transformations in simpler forms (e.g. diagonalizations, svd - presumably you'll encounter both of these in the near future)
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>>15017789
The dot product of any vector with a orthogonal basis vector would give the corresponding coordinate of that vector. But for normal orthogonal basis, you have to solve a system of linear equations to find coordinates. But frankly, this applies to any vectors, when you know the angle between the basis; right angles are just easier to work with.
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>>15017814
>normal orthogonal
Non orthogonal
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>>15017789
The canonical basis span the whole vector space, they don't span particular subspaces. Gram-Schmidt would vectors span the same subspace.
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>>15005882
are you just starting chemistry? the obvious answer is to add conjugate acid (or a strong acid) to the solution, it gets a bit complicated quantitatively
subtracting the two pH values via HH you get
$log \dfrac{[B_1][A_2]}{[A_1][B_2]} = 0.9$
so
$\dfrac{[B_1][A_2]}{[A_1][B_2]} = 7.94328234724$
the trivial solution is that $pk_a = 8.3$, then $[B_1]=[A_1]$ so $[A_2]=7.943[B_2]$,
for any given $pH_1$, $pH_2$ and $pK_a$ and defining $[A_2] = [A_1] \pm Δc$ and $[B_2] = [B_1] \mp Δc$ ($Δc$ being either strong or conjugate acid added in which case it's +/- or strong or the buffer acid in which case it's -/+) you get
$ΔpH = log \dfrac{[A_1][B_1]\pm[A_1]Δc} {[A_1][B_1]\mp[B_1]Δc}$
or
$ΔpH = log \dfrac{ \dfrac{[A_1][B_1]}{Δc} \pm [A_1]} {\dfrac{[A_1][B_1]}{Δc} \mp [B_1]}$
via HH we can also get that $[B] = 10^{p_H-pK_a} * [A]$ so in the end:
$ΔpH = log \dfrac{10^{p_H-pK_a}*[A_1]\pmΔc} {10^{p_H-pK_a}*([A_1]\mpΔc)}$
i'm at my wit's end here, maybe some mathfriend can help? drawing the function in desmos gives https://www.desmos.com/calculator/fwtrc7j3uj, changing the $pH - pK_a$ part seems to minimally change the graph but $b (Δc)$ and $[A]$ (the x-axis value) don't, i honestly thought the concentration would cancel out and my gut feeling's telling me that as long as both $p_1H$ and $p_2H$ fall within the buffer range ($pk_a\pm 1$), $Δc$ remains constant for a constant $ΔpH$
looking back the answer's probably just saying conjugate or strong acid
side note: i've never seen anyone spell Hasselbalch's last name correctly, not even the professors
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>>15004641