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/sci/ - Science & Math

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Formerly >>15128726

>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
annas-archive.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

Tips for asking questions here:
>attach an image (animal images are ideal, you can grab them from >>>/an/. Alternatively use anime from safebooru.donmai.us)
>avoid replying to yourself
>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:
>>15131187
>>15133763 [1]
>>15136931
>>15141449
>>15147231

Chemistry questions:
>>15129501
>>15131403

Biology questions:
>>15133493
>>15140285

/g/ questions:
>>15145059

Stupid questions:
>>15130859
>>15132122
>>15133336
>>15135401
>>15136101
>>15136300
>>15139626
>>15139633
>>15142288
>>15145697
>>15146484
>>
if a square matrix has a right inverse does that imply it also has a left inverse which is equal to the right inverse which is equal to the inverse of the matrix
>>
>>15147231
Personally, I really like Grimmett & Stirzaker's Probability. See if you can solve that, if it's too hard for you, use Feller.
And I recommend you don't read that garbage book that is Casella & Berger, but I can't suggest any non-measure theoretic alternatives either. I have heard some anons say good things about Georgii's, Stochastics, which does probability and statistics both.
>>
>>15149576
Yes.
>>
$\displaystyle f \in C[0,\, 1] \land f \neq 0 \implies \exists\, x_{0} \in [0, 1]\, \exists\, \epsilon > 0\, \forall\, x \in [x - \epsilon, x + \epsilon]: \frac{f(x_{0})}{2} \leq f(x)$

Does anyone of you have an idea how I could prove/disprove this?
>>
I don't see why g is continuous. pls help
>>
>>15149665
Firstly $x \in [x - \epsilon, x + \epsilon]$ is a tautology. I'm sure you meant $x \in [x_0 - \epsilon, x_0 + \epsilon]$ instead.
Either way consider a function that takes negative values like the constant function $f(x) = -1$ as a simple counterexample.
>>
>>15149677
$\displaystyle f \in C[0, 1]\, \land\, f \neq 0 \implies \exists\ x_{0} \in\, [0,\ 1]\, \exists\, \epsilon > 0\, \forall\, x \in [x_{0} - \epsilon, x_{0} + \epsilon] : \biggl|\frac{f(x_{0})}{2}\biggl| \leq |f(x)|$

You're right. This is how it should have been. What about now?
>>
>>15149682
all values of f are positive or 0, so you can ditch the absolute values. This is what interests me
>>
>>15149682
>choose x_0 in [0, 1], such that f(x_0) >= f(x) for all x in [0, 1] (exists because of the Extreme value theorem)
>choose x_1 [0, 1], such that f(x_1) < f(x_0)
>define $\epsilon$ := |f(x_0) - f(x_1)|/2
>f is continuous, therefore
$\exists\, \delta > 0\, \forall x \in [0, 1]: |x_{0} - x | \leq \delta \implies |f(x_{0}) - f(x)| \leq \epsilon$
>this delta is the epsilon you're searching for
In case the function f is a constant polynomial, you'll have to find another solution
>>
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https://matheducators.stackexchange.com/questions/20649/why-do-so-many-people-hate-math
How would you answer this question?
>>
>>15149774
imo the problem is a lack of passion from math teachers. School math is taught in an incredibly boring way and this is because the teachers and the people who set the syllabus do not care about math. It is rare to find a math teacher with any further education in math. Students look up to and mimic their teachers, but now the teachers don't care and lazily memorized formulas and hate math themselves. If you want students that like math, find teachers that like math (mathematicians).
>>
>>15149669
We want to show
$\forall\, x_{0} \in D^{n}\, \forall \epsilon > 0\, \exists\, \delta > 0\, \forall x \in D^n: |x_{0} - x| \leq \delta \implies |g(x_{0}) - g(x)| \leq \epsilon\ (1)$

proof
>f is continuous, i.e.
$\forall\, x_{0} \in D^{n}\, \forall \epsilon > 0\, \exists\, \delta > 0\, \forall x \in D^n: |x_{0} - x| \leq \delta \implies |f(x_{0}) - f(x)| \leq \epsilon$
>choose a random x_0 and a random epsilon
>all x have to be contained in a delta-circle, since f is continuous
>all f(x) have to be contained in the epsilon-circle
>construct the tangents of these two inner circles, they will project onto the S^(n -1) outer circle
>the distance of the ends of this projection is the epsilon in (1); the delta in (1) is the delta we had used in the beginning
something like this, is how I would do it
>>
>>15149790
I don't think teachers are fully to blame. Some students simply don't like math, because they have other interests. They hate math, because for them it's a subject that they have to put up with in order to get to things they have more interest in or talent for. I've witnessed it many times that people actually prefer the boring memorizing/number crunch part of math because it's easier and therefore they have to spend less time on it.
>>
>>15145697
if I can't solve it after hours and I ran out of ideas on how to solve it, I look at the solution and go through it carefully
>>
>>15149669
dude just literally compute it. parametrize the line a compute the intersection with x^2 + y^2 + 1 = 0.
but you should already the see that the result will be algebraic and therefore continuous.
>>
Does the parallel postulate hold in the physical world?
Which of euclid's first 4 postulates hold in the physical world?
>>
>>15149576
The identity matrix is both a left and right identity: XI=X=IX. No other matrix is either a left or right identity; XA=A => X=I, AX=A => X=I.

AB=I => BAB=BI=B => BA=I
>>
>>15149834
undecidable, I'd say. Since we don't know if space is continuous or discrete
>>
I have 50ml of blood and 50mg of ascorbic acid (which I think is an antioxidant) if I mix them together would I be able to prevent the iron in the blood from rusting and turning brown?
The blood probably has less than a mg of iron per ml
I suck at chemistry :P
>>
>>15149490
i had an exam question which asked me to check if two matrices but i had a retard moment and forgot the core property of similar matrices and instead of checking if the trace/determinant/whatever were the same (which would have allowed me to say that they are NOT similar if they werent equal) here's what i did, can anyone tell me if it's correct anyway?

Let A and B be the two matrices
they are similar iff there exists an invertible matrix S such that $A=S^{-1}BS \\ SA=SS^{-1}BS\\SA=BS\\SA-BS=0\\S(A-B)=0$ at this point i multiply S by the matrix A-B and get the null matrix which isn't invertible which means that A and B are not similar.
>>
>>15150201
*from "at this point" and on is supposed to be after the last step
>>
I absolutely hate probability, can someone help me with two assignment questions?

"At a school there are 40% girls and 60% boys. Three quarters of the girls and half of the boys have a tablet. We randomly select a student and look at the event:

J = "the student is a girl" and N = "the student has a tablet"

a) Determine the probabilities P(N | J) and P(N).
b) Determine the probability P(J | N)."

And lastly, I've done the first part of this but the second question fucks me.

"On a pin code lock, we can see that the numbers 1, 3 and 4 are heavily worn, so we assume that the pins required are made up of those three numbers"

B) If the code has four digits: how many different 4-digit codes are there, that only
using the digits 1, 3 and 4? (NOTE: make sure you actually use all three of these digits!)
>>
>>15150222
b) is 1/2.
10% are girls with no tablet
30% are boys with no tablet
30% are girls with tablet
30% are boys with tablet
We sum up the latter two categories to make 60%.
So P(J | N) = 30%/60% = 1/2

B) is 36.
We know that one of the numbers is used twice, and the other two once each. So that can be any one of the three numbers.
We then find the number of possible combinations given two of one number, and one each of two other numbers. That's 4!/2! = 12.
So the answer is 12*3 = 36
>>
>>15150201
Matrices are not commutative
S(A-B) = SA-SB, this is not usually equal to SA-BS
>>
>>15150337
Ahh now it makes sense.

In B), how do you calculate that it's "4!/2! = 12."
4! because of the 4 possible digits and..2! from... what?

12*3 is understandable, where the "3" is the number of digits, correct?
>>
>>15150410
Yes.
>2! from... what?
One of the numbers is duplicated, so it's actually 2!*1!*1!.
>>
Do magnetron sputter chambers "burn" all the process gas, or do they passivly vent the excess gas into the atmosphere?
>>
>>15150450
Thanks, anon.
>>
>>15149803
I agree, I don't know about other countries, but here there we have a mathematical literacy subject from grades 10 to 12 for people who won't need real math later. I think this is a good idea. But the problem persists in the real math classes and even calc and linear algebra where the students /should/ care. Another problem is that students often approach the subjects with the single goal of getting good grades (or merely passing; equally useless), this again is something that got reinforced from a young age, but this is also a problem outside of math.
>>
>>15149889
I might be a math guy with a touch of chemistry
knowledge, but iron doesn't rust in the blood.
>>
What is the best Touhou OST?
>>
>>15151756
PoDD or LLS. No competition
>>
Mathematically speaking, how do I find love?
>>
This professor never taught us anything for weeks, then decided to drop this yesterday. Help me pass this class pls
>>
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>>15149490
Good Morning /Sci/entists!

I am working on a long latex document. Somehow I introduced a compile error. I removed the new text I added, but still the error happens. What is the best way to debug latex? TexWorks isn't giving me much info and the console output may as well just say "lol nope".

Thank you /Sci/entists for reading my post.
>>
>>15152167
You want to make maid generators or whatever, and you can't even compile a $\mathrm \LaTeX$ code?
>>
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what even is this
>>
>>15152174
What? These have obvious counterexamples.
>>15152165
>professor didn't teach so I won't study
People like you are sad.
>>
>>15152180
Yeah they're obvious, but I wouldn't have asked if I wasn't so stupid
>>
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>>15152173
Using a language I made is an easier task for me than using a language someone else made. It either does what I think it should do the way I think it should do it, or it gets changes until it does.

I guess I can try to make some kind of typesetter other than latex, since all I really need is a PDF with maids in the margins and also draw Maid Space like a 2d array of black and white pixels?

With latex I am just stealing from how matrices are printed, but changing the number to square or blacksquare. I think it looks nice.

I don't know if I can make latex draw it like it is drawn in the attached image.
>>
>>15149490
Is 'metric' in Real Analysis related to tensors? If so, how?
>>
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>>15152167
The solution was delete an aux file. I am going to return to using my Writing Computer now. I don't know what an aux file is, but it was mentioned in the TexWorks console and it kept referencing text I had already deleted and something about getting a runaway.

>tl;dr: If you get the same problem, deleting the aux file and restarting TexWorks fixed it.
>>
>>15152167
>What is the best way to debug latex?
Same way you debug any language, really:
>read the logfile (it has file extension *.log)
>delete and rebuild all intermediate files (including the index/bibliography/whatever else you happen to have)
>isolate to a minimum reproducible example (ideally with at most one instance of \usepackage)
>google the error message (or check TeX SE)
>read the package documentation and (as a last resort) source code
>>
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>>15152239
I guess this is a good workflow to debug a program if you don't have any tools capable of actually debugging a program? Ideally you'd click by a line of text and it makes a breakpoint and you run a debugger and go in the breakpoint and see what is happening.

I guess Latex never implemented something like this because it is very old?

Either way it works now. Just had to delete some files. I think it was either caching or building something wrong in an aux file and deleting that made it happy.

I am not entirely sure what an aux file is but that is my guess and I don't have to care what it is now because document compiles again and looks how I want it.
>>
>>15152212
No more than distance in general is, because a metric is literally just a generalisation of distance
>>
Help me /sci/. I have to pass either Algebra or Logic to finish my bs in comp. science.
What are your learning techniques? What are good books/resources for those two subjects?
I am desprerate here.
>>
good books that provide an introduction to mathematical proofs?
>>
>>15152391
>>
>>15152401
>>
>>15152379
There is a nice logic book called Symbolic Logic by Copi. Also there are nice YouTube series about it. Logic is fun and if you can only take one class I recommend that one because symbols look cool.

I would link the book but z-library died and I am not sure how to operate whatever replaced it. I have a paper copy of the 5th edition.
>>
why do some bodily fluids have slimy texture while others are more fluid like pee?
>>
Suppose that an oscillator, i.e., a mass attached to a spring, has a certain resonant frequency. Why does the resonant frequency becomes zero if the spring is cut? I would say that it should simply become a meaningless concept. I don't get why it couldn't be infinity rather than zero.
>>
what's the theorem you proved yourself that you're the most proud of?
>>
>>15152416
Terrible suggestion. Your book is written for high schoolers.
>>
>>15152391
"how to think like a mathematician" by Kevin Houston is what I used. But it's a book not only about proofs but also other techniques that you'll likely need for doing university-level math. It doesn't provide solutions to the exercises, however
>>
What is the most offensive way to call a black person on the internet?
>>
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>>15152174
>(c)
>>
>>15152737
i came up with a new (to me) proof of concept eulers identity one time. the thing im most proud of is discovering markov chains before i knew what they were.
>>
GLOBALIST SCUM YOU WILL NEVER TAKE MY LANGUAGE YOU WILL NEVER TAKE MY PRIDE YOU WILL NEVER QUENCH ME INTO YOUR GAME I FUCKING HATE YOU DEATH TO THE ANTI CHRIST GOD IS GREAT FUCK YOU FUCK YOU FUCK YOU GLOBALIST SCUM FUCK OFF BACK EPSTEIN ISLAND YOU HOLLYWOOD PIECES OF SHIT
hello friends
>>
>>15152769
>/sci/ - Schizophrenia & Meds
>>
>>15152774
The truth hurts innit
i'll be of in a yurt in kyrgyzstan while you lot obey your devil worshipping overlords.
>>
>>15152744
That seems appropriate for someone with no prior knowledge trying to start a new subject?
>>
>>15149669
Because $x \to (x, f(x)) \to g(x)$ is a composition of continuous functions.
>>15149790
Couldn't have put it better myself.
>>15149803
No, middle/high school maths fucking sucks, if you enjoyed applying the fucking Bhaskara formula you are literally an unathletic, limp dick faggot who likes the only subject he's good at.
>>
What is 3x+1, literally? It's a four symbol-long string but it's also a line in R×R and a sheet in C×C, what is really going on?
>>
>>15149490
taking undergrad diff eq this semester and unfortunately im stuck with a bad prof. What resources do you guys recommend for self learning the material?
>>
$\gamma \notin \mathbb{Q}$
Go!
>>
>>15152956
same name for different things.
>>
Jean is shorter than Brutus but taller than Imhotep. Imhotep is taller than Jean, but shorter than Lord Scotland. Lord Scotland is twice the height of Jean and Brutus combined but only one-tenth of the height of Millsy. Millsy is at a constant height of x − y. If Jean stands exactly one nautical mile away from Lord Scotland, how tall is Imhotep?
>>
Does the Laplacian on a Riemannian manifold have no positive eigenvalues? If yes, this be shown with Hodge theory?
>>
>>15153278
>this be shown
*can this be shown
>>
>>15153278
>Does the Laplacian on a Riemannian manifold have no positive eigenvalues?
It can if the manifold isn't compact. $\Delta e^x = e^x$ in $\mathbb{R}$, for example.
>If yes, this be shown with Hodge theory?
I think you just used the Green identities.
$\displaystyle \int_U \psi \Delta \psi + \| \nabla \psi \|^2 \ dV = \int_{\partial U} \psi (\nabla \psi \cdot \vec{n}) \ dS$
Right side zeroes because compact, pass stuff to the other side, bada bing bada boom.
There might be a Hodge theory proof tho.
>>
>>15153313
>Right side zeroes because compact
Is that always true even when U has a (nonempty) boundary?
>>
What is an electrical component that uses power called in English? What's another term for a resistance that is doing something practical, like a bulb. Something like "user"?
>>
>>15153326
Sorry that was a stupid question
>>
how do I stop feeling lonely?
>>
>>15153392
Touch grass.
>>
>>15153395
but I do that every day
>>
>>15153327
>>
>>15153453
Thank you Sir
>>
>>15152653
How long does it take for the mass to return to it's original equilibrium position?
>>
>>15153150
>Jean is ... taller than Imhotep.
>Imhotep is taller than Jean.
?
>>
>>15153150
How did you choose those names?
>>
>>15153467
you heard right, Chud. She can be any height, she wants. This called liberty of expression, you asshole bigot
>>
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>find a "solution"
>take a look at the textbook solution
>it's five times bigger
>>
Does every real-analytic function R --> R admit a holomorphic extension to some open neighborhood of the real line in the complex plane?
>>
>>15152401
>>15152407
>>15152748
thanks anons
>>
Can you lads tell when I'm posting with some alcohol in my blood?
>>15153326
>>15153342
No, no, my mistake, I should have written down closed instead of compact.
For compact manifolds with boundary you can have stuff like $e^x$ restricted to $[0, 1][math]. Of course, if you're working with a class of functions that ensures the border integral still zeroes the result still works. >>15153661 Yes, because the power expansion at the origin has infinite convergence radius, hence the function is actually entire. >> >>15153795 >Yes, because the power expansion at the origin has infinite convergence radius, hence the function is actually entire. No, nevermind, I'm wrong. The result is still true because if the function is analytic you can power expand it at each point of the real line and the expansion needs to be well-defined on an open set around the expansion point. Then we can take a convex subset of that open set. >> I don't know how to do my quantum mechanics homework. It's the final course I need to graduate. I'm fucked seriously, what do I do? Do I bite the bullet and pay for chegg? >> >>15153847 Can’t be that difficult, post it here and let’s see >> >>15153577 >within an order of magnitude eh not bad, champ! >> File: 1674606061559.png (101 KB, 790x760) 101 KB PNG >>15153979 >> can I define the set of Fermat numbers as [math] \{m \in \mathbb{N}^0 | 2^{2^m}+1\}$?
>>
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>>15154159
im too lazy to do this but for problem 1 at least, to find the expectation value you need to work out what the vector-matrix-vector multiplication $\ev{\hat{S}}{s,,m_s}$ is (but i think you probably know that already). do you know what $\ket{s,,m_s} = \ket{\frac12,,-\frac12}$ means? what's another name for this state that you might be more familiar with (hint: they are normalized eigenspinor of something)?

I *think* for this one you're supposed to use the spectral decomposition of the operator but its been a while since ive taken a QM course lol so gl
>>
>>15154222
woah, goofy 4chan latex is goofy. rip packages. Let's try that expression again. first expression is
$\braket{s, m_s|\hat{S} | s, m_s}$
and the second onr that didnt render is $\ket{s,,m_s} = \ket{\frac12,,-\frac12}$
>>
>>15154170
almost, but your set builder notation is backwards; the part before the bar is the number that actually goes in the set, the part after the bar is the condition. just swap them around
>>
>>15154170
Please use \mid next time anon-kun desu ne.
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>>15154159
1) : write Sx and Sy in terms of the Sz basis, then sandwich the state you were given around that

2) : write Sy in the Sz basis, and do <X|Sy>

3) : perform the dot product in H to get the hamiltonian as a function of the i coordinate (why do they switch between i and x for this problem? retarded). convert this into the z-basis and then exponentiate this operator as U(t)=e^-iHt/hbar (you should know how to exponentiate matrices, no?). then perform <-|U(t)|+> where -, + are the spin-down and up eigenstates

4) : swap this B-field for that in problem 3, do the same steps but now it's easier to convert the hamiltonian from z-basis to y-basis since your initial state is in the y-eigenbasis
>>
So why is movable type called movable? I thought the type moves somehow, but from what I see, someone has to arrange the type required for each page by hand anyway. So what's unmovable type?
>>
>>15154369
>So what's unmovable type?
Carving a body of text into a single wooden block, for example, and then using that block to print. Movable refers to modular characters or words that can be rearranged to print a variety of documents.
>>
>>15154383
Why would they do that? Were they fucking retarded? The le greatest invention of 15th century was figuring out that by carving only the letters, you could move them around and reuse them? What the fuck?
>>
>>15154396
>Why would they do that?
Because it is an improvement over copying a document over and over by hand.
>>
>>15154396
>was figuring out that by carving only the letters
not that, how. gutenberg's major innovation was not the concept of letters, it was figuring out how to cast metal ones

also, basically nobody could read in 12th century europe. there was even elitism that basically nobody SHOULD read. in that environment, when all you ever want to produce is one bible, type is questionably even worth it if you have it. demand only came about due to rising literacy rates
>>
What is mold made of?
>>
>>15154407
>>15154429
How is it Gutenberg's method different from hot metal typesetting?
>>
>>15149828
>the result will be algebraic and therefore continuous.
sorry for another stupid question, but can you elaborate on this (or refer me to something to read)?
>>
I'm designing an electronic submarine with its depth operating by ballast which displaces water with an electric motor.

Is my motor going to have to work harder at lower depths?
intuitively I think it would because of the pressure, but it seems like buoyant force should be working in my favor, and I'm just pushing up to displace water. I'm really hoping that's right because it would mean I can go way deeper.

Am I retarded?
>>
Can anyone answer me a few questions about writing a paper?

If certain document states something and provides the reader with the sources used to make such statement, it would be correct for me to cite such statement as done by the author?
Might sound stupid as the autor of the paper is the one that made the statement, but I need certainty

If i happen to copy several sources that are making up the structure of another paper because my topic is similar enough, would that count as plagiarism?
I'm not taking their conclusions as mine, only their sources. Still, I wonder if I'd need to check the sources myself to get at least a new interpretation of the content

And, what should I actually be looking inside a scientific document in general?
Can I cite anything?
Or it should be correct to only cite the conclusions of a document?

Not my area, but it's needed to cite anything math-related such as the authors of formulas if I want to write let's say an statistics manual?
Besides the formulas that have an known author, if anything

Any more tips on how to actually write a document are welcome, as I have only found information on the basic structure and planning of scientific documents.
>>
>>15152885
Not that anon, but it literally is a book for high schoolers, not to mention, outdated.
>>
I've been thinking about Boy Girl paradox ("at least one" version). Following order of operations, you end up with 25%. Not following order gives 50%. Then there are those who are wrong and say it's 33%, by thinking BG and GB are different in an unordered example. Saying they're different means you care about the order, but they still insist on not following order to get the result.
So my question is, is there a name to this fallacy, which I could best describe as "applying ordered probabilities to unordered events"?

Also, don't bother trying to bait me into an argument about logic. It's not really relevant to the question anyway.
>>
>>15154705
>Is my motor going to have to work harder at lower depths?
Yes.
>>
Is there a simple function $f: \mathbb{R}^2 \to \mathbb{Q}$ such that it returns any rational within a line segment denoted by two real numbers?
Obviously you can use the axiom of choice to take such a function but I was wondering if it exists even without the axiom of choice.
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>>15154960
A simple function can only take on finitely many values.
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>>15154981
I meant simple in the colloquial sense, as in possible to write down using elementary functions by hand.
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>>15154960
Given two real numbers a and b, represent them both in binary and look for the first place where they differ (i.e. where a has digit 0 and b has digit 1). Then truncate up to that digit (i.e. get the common initial prefix of the binary representations of a and b) and you have a (dyadic) rational in betwen them.
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>>15154996
This only works for pairs of reals where at least one is definable, not all pairs of reals.
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>>15153460
Makes sense, thank you
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>>15154981
>>15154987
the absolute state of mathschizos lol
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>>15149490
is there a standard for logical notation? I have a set of symbols I tend to use from one of the books I learned logic from, but it seems like different books disagree. Are all equally valid, or is there some set I should write with if I want to talk about logic in public?
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>Intelligent calcium is not intelligent in the sense that you or I are intelligent, but intelligent in that it is sentient. I.e. it is aware of itself and its surroundings. It is also able to communicate this awareness in human terms.
How exactly is this different from human intelligence?
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Can someone tell me how to translate between QM notation and Statistics notation?
I've never formally learned statistics and I'd really like something like those simple tables that go
>linear velocity | angular velocity
>v (m/s) | omega (degrees/s)
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Is smoking is really so bad for you when there are so many smokers who don't die of lung cancer?
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am i supposed to do all of these. and in what order
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>>15155493
Yes it's very bad for you. It massively increases the risk of various diseases and afflictions. So sure, some old codger may pass away peacefully and unaffected after smoking like a chimney since he was 15 but at least half a million deaths each year in the US alone are directly attributable to smoking.
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Are hyperoperations useful for anything? Does hexation or any other hyperoperation have applications?
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A while back some anon shared a link to a blog that detailed why Graham Hancock's new "history" show was trash. The blog went into great detail on this and I want to find it so I can convince some of my more gullible relatives this is all trash. Does anybody here have a link?
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>>15155453
are you taking about Look Around You? you know that show is a parody, right?
>>15155567
calc 1, AB, and dif calc are all the same same
calc 2, BC, and integral calc are all the same thing
just go top to bottom, skip stuff you already learned
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if i have two planes in 3D space, and one of them is an affine plane (i.e. it has an origin and two axes), how can i find the intersection of the two planes in terms of the coordinate system of the affine plane?
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How much can you learn about a subject just by reading a wikipedia article on it?
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>>15156329
Just like reading the definition and examples given in the textbook or sometimes just as in lectures
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>>15156329
wikipedia is a very terrible learning source. not that its incorrect, but it only really lists definitions for things and doesnt provide any sort of intuition or motivation.
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>>15156329
Most of the time, extremely basic stuff, broken links and not the best sources
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What to do after calc 3 and linear algebra?
CS/Math freshman
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>>15156530
analysis, modern algebra, algebraic geometry
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>>15155460
what kind of notational things are you curious about? "QM notation" is not specific enough
it sounds like all you need to do is know how to translate bra-ket notation into integrals, which is covered in chapter 1 of most QM textbooks
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>>15156530
actually start applying it
also ODE/PDE's
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>>15154773
>it literally is a book for high schoolers
That seems appropriate for someone with no previous exposure to the topic?

>not to mention, outdated.
How? It isn't like math expires.
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What is physics?
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>>15157142
nooooo you have to use the most obtusely written formal logic based book for graduate students, also that'll be $199.99 goy! >> File: 1656738888839.png (140 KB, 640x830) 140 KB PNG I don't understand this assignment in Scratch, Is anyone good at it here? "Adapt the program above to find how many different pairs of numbers (i, j) exist such that i < j. How does this change when you change the constant "muligheter"? Can these numbers be associated with any "Combination Numbers" (kombinasjonstall) we've worked with? ((I think combination numbers is basically Pascal's triangle, but I am unsure)) Scratch translation: Muligheter - Possibilities Antall_kombinasjon - Quantity (of) combinations >> >>15149490 Good Morning /Sci/entists! >Why I am asking the question I am writing more in my Maid Space book to make ideas sharper before making some of them into Java 18 code. Remaining work is finish writing and then add a lot of images of maids in all the margins and also make Maid Cards to distribute the software. A lot of times, I use$\square$to make a square □ and$\blacksquareto make a black square ■, because that is nicer than looking at 0 and 1 a lot of times if you want to see what a Coolkyousinnjya Maid Space looks like. I need more colors for squares so I can have a higher amount of colors to use as squares and counting or uncounting with a Maid Space that has a higher radix than 2 can be done in a way that looks nice. Worst case I can use other symbols like maybe a circle and a black circle or something but colors would be preferred for readability. I am trying to design the book to look like a Wolfy book so it can have high gloss paper and a hard cover and a lot of colors and images and look nice when it gets printed. >The question How can I get more colors for the squares in latex? I want a red one and a yellow one and a green one and probably other colors too. Thank you /sci/entists for reading my post. >> >200 seats at a theater >15% of all spectators want drinks >how many drinks do you have to get, so that you can provide a drink to each spectator with a 90% certainty I evaluated it by >graphing the binomial distribution B(200; 0.15) >taking the integral up to a natural number n, at which the integral is greater than 0.9 But how can you calculate this effectively without graphing? >> File: 1670525557951095.jpg (195 KB, 745x1151) 195 KB JPG >>15157332 Do you have to use this language? It looks like someone made a worse version of DRAKON on purpose. I did not know there were visual programming systems that made visual programming so visually unappealing. Your Computer Program looks like a road cone. >> >>15157385 Yes, I sadly have to use Scratch because the course demands it. Trust me, we all hate it. Makes it even worse when we have to teach it to elementary school kids. >> >>15157396 Are you stuck with the road cone coloring? Also, please rename i and j to make them more descriptive. It will improve readability in your example. As will abandoning German or Swiss or whatever language is making words like "muligheter". Why does it say change by one? Change how by one? >> File: 1668129001848.jpg (56 KB, 750x750) 56 KB JPG >>15157417 Yes, I am basically stuck with the template and am only allowed to change the parameters. Not allowed to rename "i" and "j" Abandoning Norwegian would probably help, I just copy-pasted it from our assignment sheet. > Change Don't really get what you mean here, it changes the "j" and "i" variables by one? >> >>15147231 You would have to look at introductory books on combinatorics. They will probably have a few introductory chapters on counting &c. >>15154838 First of all, unconditionally the chance is 25%, and the information "at least one" means it must increase (to 33% or 50% depending on your interpretation). There is not really anything special going on concerning order; people will just make up whatever additional assumptions they think are needed because the problem is too vague at the start. I cannot think of a name. >>15157343 \usepackage{xcolor} and then {\color{red}\blacksquare} should work. >> Any good books that combine higher mathematics with evolutionary biology? >> File: file.png (48 KB, 1176x205) 48 KB PNG >>15149490 Total retard here. Could anyone explain what the fuck is going on here? Of course I'm aware that cosine is the derivative of sine, but why is the step after that, apparently utilizing the chain rule, happen? >> >>15157384 Use the normal approximation https://stats.libretexts.org/Courses/Las_Positas_College/Math_40%3A_Statistics_and_Probability/06%3A_Continuous_Random_Variables_and_the_Normal_Distribution/6.04%3A_Normal_Approximation_to_the_Binomial_Distribution >> >>15157384 What is the probability any number of seats is filled? Is it fixed that 15% of spectators want drinks, or does every spectator decide after arriving, with a 15% chance of ordering one? Assuming the obvious assumptions you did it right, if it is a problem for school look into 'the normal approximation to binomial'. Also, you don't need to graph to integrate. In something like R, this is just qbinom(.9, 200, .15). >> >>15157591 Look in reverse; what is the derivative of (sin x)**2? (Use the chain rule) >> >>15157594 >>15157601 thanks >> File: pressure switch2.jpg (1.78 MB, 3264x2448) 1.78 MB JPG How does electricity work? I posted a bread on /diy/ but asking here too in case /sci/ knows more. I want to understand hot vs neutral wire, and why there are two ground wires to my pressure switch instead of just one. Full details of my question here: >>>/diy/2550788 thanks >> how would you simulate stellar bodies interacting with each other the same way they do in reality? Like if I want to simulate the moon orbiting the earth, I'd create 2 pairs of point + velocity vectors, position them and set an initial velocity, then each time step update position based on velocity, and update velocity based on current velocity and position relative to the other object(s) factoring in mass. The problem here is that reliance on position and this 3rd person reference frame. obviously it doesn't exist in reality, same with orientation. There are no coordinates to position things at, and you can't move the moon in the '+x' direction. So how do I get around this? how do I have orientation-less, position-less points that can interact with each other to change their relative distance to each other? I can think of just storing distance from any point to every other point, but then you need to be able to manipulate that, like in an elliptical orbit, distance would be some function that oscillates between 380k km and 390k km, which seems simple, but then as soon as you add another point into the mix, it's not so simple any more >> hello smart anons, thank you for helping dummy former neets like me get through college. Have a nice day. >> >>15157752 You are right, all velocities are relative. However acceleration is not, and you can't have orbits without acceleration (gravity). The simulation each time step will calculation velocities (and hence position updates) based upon the total acceleration (force) acting on the body. >> >>15157724 that anon in your thread gave that correct answer. one ground is "input" and the other is "output". its just so you can provide ground to your pump. as for the difference between live, ground, and neutral, live is the positive voltage, ground is zero volts, and neutral is the negative voltage. imagine if you stacked two AA batteries on top of each other. measuring the voltage from the middle node (where the two batteries meet) to the top would be 1.5v, and measuring from the bottom to the middle is also 1.5v, but measuring from the bottom to the top is 3v. thats basically whats happening when youre measuring 110v across live/neutral to ground, and 220v measuring from live to neutral. they're two sin waves that are 180 degrees out of phase (flipped over, basically), so you get double the voltage. three-phase power is also common, which would be a sin wave thats 120 degrees out of phase with live, which ends up with $110\sqrt{3}$ volts, which is like 170 or something. >> >>15157789 >The simulation each time step will calculation velocities (and hence position updates) based upon the total acceleration (force) acting on the body. how would it do that though? Like if I'm thinking of 2 points "orbiting" each other, from the perspective of each point, there is no motion at all, they are both perfectly still in relation to each other and are not moving closer despite the mass they have that should be pulling them closer. (I'm assuming orbits still make sense with points, real stellar bodies are composed of many points so an orbiting body grows closer and further away from each of those instead, maybe I can't make this assumption however?) you also can't store velocities between time steps since it's not a real property. I suppose maybe you could infer it? if the distance equation doesn't change despite the acceleration, then there must be some movement between the 2 points, and I guess the direction of that movement is irrelevant until you insert another point to 'triangulate' the movement also aside, but I'm guessing the concept of movement doesn't exist in a single point system (does time even exist in such a system???) >> >>15157792 > as for the difference between live, ground, and neutral, live is the positive voltage, ground is zero volts, and neutral is the negative voltage. This is nonsense. Neutral and ground are at roughly the same potential (they're connected together at the main board). The difference is that neutral carries the return current, ground isn't supposed to carry any current. Any exposed metal (e.g. casing) is supposed to be connected to ground so that if any live part comes into contact with exposed metal, it trips a fuse or breaker (but if there's a RCD, that will trip first). >> >>15157833 i dont think thats true. its common to ground casing for that reason, and ground usually isnt supposed to carry any current, but in the US (i suspect youre a bong since you called them RCDs instead of GFCIs) you arent gonna trip any breaker or blow a fuse if you run current to ground. OP said it himself (in the other thread): >Touching one of the leads to the input neutral and the other to ground or output also gave me 110V. if you have a washing machine power outlet that you can probe youre welcome to go see this for yourself. in regular power outlets, live and neutral are identical. >> >>15157829 > Like if I'm thinking of 2 points "orbiting" each other, from the perspective of each point, there is no motion at all, Incorrect. The motion is the same as one point orbiting the other. The distance doesn't change, the direction does. > you also can't store velocities between time steps since it's not a real property. Also incorrect. Essentially, you need to choose a coordinate system. The choice of coordinate system doesn't matter, as the laws of physics are invariant under change of basis. But you need to parameterise the space. >> >>15157855 >live and neutral are identical. ground and neutral* >> File: 1672387708198029.png (493 KB, 637x762) 493 KB PNG >>15157575 Thank you for telling me. This worked and I can now make red square. I am going to look for documentation to xcolor to see what other colors I can make my squares have. >> >>15157792 Thank you. As I also said in the other thread, I am still confused on ground in the pressure switch setup. It is my understanding that the ground wires are so that if there is a fault causing electricity to flow into the pressure switch's metal body, the ground wires will carry it into the ground so that if a person happens to be touching the switch's metal body, they don't get as much electriciy flowing through them. In which case why does it need one ground wire going to the panel and one to the pump when they're both just for safety at the switch? Or am I completely wrong about them being for safety right at the switch? And regarding hot vs neutral, both are carrying current in the same direction (from my panel to my switch) correct? I don't fully get what the difference is between "positive" and "negative" voltage. Even with magnetic polarity I don't really get it, is it just arbitrary what we have always defined as "positive" vs "negative"? >> >>15157855 > you arent gonna trip any breaker or blow a fuse if you run current to ground. Shorting neutral to ground won't blow a fuse (but will trip a RCD). Shorting live to ground will blow a fuse for the same reason shorting live to neutral will. > OP said it himself (in the other thread): > > Touching one of the leads to the input neutral and the other to ground or output also gave me 110V. That's not neutral. In the US, a 240V appliance has two live ("hot") wires (which are 180° out of phase) and no neutral. Neutral is (nominally) at ground potential, although it might differ by a volt or so due to the neutral current and Ohm's law. >> >>15157142 >That seems appropriate for someone with no previous exposure to the topic? How so? It doesn't cover a ton of material in the undergrad curriculum. >How? Logic is an area that changed a lot in the past 50 years. Reading a book that doesn't include, let alone comment on these changes, is stupid, specifically when taking a logic course in the 21st century. Better to just read a modern book like Ebbinghaus, you know, something actual to-be-logicians read. There even is the saying "back to Ebbinghaus". >>15157304 Don't strawman me, you racist retard. Not to mention, Ebbinghaus is 10 bucks new. For Copi's book you can only find more expensive, used copies. >> >>15157873 >In the US, a 240V appliance has two live ("hot") wires (which are 180° out of phase) and no neutral. i have never heard that nomenclature before. >> >>15157857 no way to do it without coordinates? Whole reason I was trying to do this is because reality doesn't have coordinates. where would you even align them? a point has no concept of up or down >Incorrect. The motion is the same as one point orbiting the other. The distance doesn't change, the direction does. I don't really get this. like if I consider a scenario of only 2 particles in the entire universe orbiting each other, the only thing they observe about the other is mass (which results in an acceleration towards) and the distance to (which determines how strong the effect of the mass is). They don't have orientation themselves so they can't position the other particle relative to anything on themselves, and there is no external reference frame to say that an orbit is occurring. the particles view of the universe is that there is another mass pulling on it and despite that it doesn't not get any closer. this is enough info to say one or both of them is "moving" but no direction can be established. would you just have a directionless velocity or something instead? I don't really get it >> >>15157887 Neutral is called "neutral" for a reason. If you touch it and it hurts, it's live/hot, not neutral. That's still true if the other wire is also live/hot. >> >>15157894 > Whole reason I was trying to do this is because reality doesn't have coordinates. Reality doesn't need coordinates; a position ... "is what it is". If you want to model the system numerically, you're going to need coordinates. The choice of basis is completely arbitrary, but you do need to choose one. > They don't have orientation themselves Are you quite sure about that? If you draw a diagram where particles are modelled as spheres, then their orientation won't show up in the diagram. But choosing to ignore orientation isn't the same thing as not having one. >> >>15157894 > They don't have orientation themselves so they can't position the other particle relative to anything What has orientation got to do with the direction they feel a gravity acting on them? > there is no external reference frame to say that an orbit is occurring Not true. An orbit means their velocity vector is changing, which means there is acceleration. If they experience acceleration they feel a force. This is precisely what centripetal force is. >> >>15157922 >Are you quite sure about that? If you draw a diagram where particles are modelled as spheres but I'm modeling them as points, dimensionless points. doesn't the fact that they are dimensionless preclude them from having orientation? orientation after all must be relative to something. a sphere has many points on it's surface and interior, it takes up space and the points inside and on the surface exist and different positions in space so it can be oriented. but a point has nothing to be relative to >>15157925 >An orbit means their velocity vector is changing A velocity vector you can't have without some sort of orientation to align it to, and some coordinate system to set it in. the crux of my problem >> >>15156982 No, translation bra-ket notation into statistics notation. Like is <A> is E(A)? etc. >> what are some midwit-alert/pseud-giveaway stupid math-related questions you should avoid at all costs when talking to a professional? >> File: 1669448198667939.png (1.75 MB, 2727x3416) 1.75 MB PNG >>15157878 >For Copi's book you can only find more expensive, used copies. I got mine for4 as part of a buy one, get one half off deal. The original price was 8. Most used books are not expensive. I have never heard of Ebbinghaus, but if his book is so cheap I will get a copy. Thank you for telling me. >> I don’t FUCKING understand diodes. Please explain it to a retarded person >> >>15157952 logarithmic current to voltage converters, with a ~0.7V drop at most practical currents (1mA-1A) >> >>15157952 Valve that only lets thing go from one direction to the other, but if you put too much pressure in the reverse it breaks. >> >>15157940 > a sphere has many points on it's surface and interior That's why all calculations use centre of mass for simplicity. No matter the shape of a body you can perform all calculations as if all the mass was concentrated at a single point. They are mathematically provable to be equivalent. >>15157940 > you can't have without some sort of orientation to align it to Not true. The vector still exists, a coordination system is only used to describe it. >> >>15157952 What kind of diodes? You need to be for specific >> >>15157962 >>15157958 Is this accurate >there is a neutral middle area that resists current flow >with forward bias, positive charge is applied to the positive side & likewise to the negative side, which causes the neutral middle ground to shrink >with reverse bias, negative charge is applied to the positive side & V/V, which causes the neutral middle ground to grow and resist more current >when the neutral middle ground shrinks to nothing, there is nothing to resist current flow >> >>15149490 Is there empty space inside water? Like, if I mix a teaspoon of sugar or salt into a cup of water, does the volume of the water increase exactly as much as the volume of the salt/sugar added? Why/why not? >> >>15158011 Dissolving is the acting of breaking apart the sugar / salt crystals so you're left with disassociated molecules. The mass will increase and I'd normally expect the volume to fractionally increase too. But it's water and water is fucking weird. So if under certain conditions and concentrations of the soluble the volume actually went down I honestly wouldn't be surprised. >> >>15158011 >does the volume of the water increase exactly as much as the volume of the salt/sugar added no. solid sugar, liquid water, and dissolved sugar (coated in water molecules) all have significantly different densities, the overall volume is not preserved. >> >>15158064 So if I dump a cup of sugar/salt in a tub of water and stir. The water volume does not increase by one cup? Sorry kinda difficult to understand what you said. Hence I gotta ask again >> >>15158102 right. also remember sugar crystals have empty space between them, so it's not really a cup to begin with. >> >>15158124 what if I use melted Sugar? >> >>15157945 >don't say you hate(d) math >if the extent of your math education is calculus, don't pretend you know anything >don't mention the axiom of choice >don't say shit of the form "i don't believe in <math thing>" >don't say anything about gödel's incompleteness theorem >stay away from retard arguments such as 0.999... =/= 1 or 1+2+3+... = -1/12 >> >>15158210 People are arguing, somehow, that 1+2+3+...=-1/12? >> >>15158212 if you analytically continue the reimann zeta function, you get zeta(-1) = 1 + 2 + 3 + ... = -1/12 >> Just found my notes from back when I was 12 and my handwriting is way better than it is at 24. You'd think the ages were reversed comparing the handwriting. What could cause childhood handwriting being better than adult handwriting? >> >>15158345 Getting comfortable As a kid writing was hard so you focused on it, now you just do it. But in turn you do not get as high quality >> File: sci.png (19 KB, 541x165) 19 KB PNG The second product of the second equation (in picrel) is wrong isn't it? >> >>15158811 No. You've overlooked the fact the bar means the conjugate. >> File: scii.png (2 KB, 199x129) 2 KB PNG >>15158820 but complex conjugates distribute over multiplication and subtraction/addition so it shouldn't matter? >> >>15158860 Yes but you are conjugating the entire expression which includes the i's. >> >>15158876 Oh, I see. Thank you! >> File: 1674853110629318[1].png (55 KB, 1132x384) 55 KB PNG Is it A or B and why? >> >>15158983 A, it's closer to the pivot point so it's less likely to turn the front of the boat towards the canal bank. >> >>15159063 Where is the pivot point, approximately in the center of the boat? I don't get this, why would the boat turn if there is no flow, and you are just pulling the boat by the bow? Is it because it is less "stable" in that case? So the most stable tow point would be right in the center of the boat? These people are doing it wrong? That's how I would do it too. >> File: Unknown-1_RT[1].jpg (186 KB, 911x1024) 186 KB JPG >>15159107 forgot pic >> >>15159107 > approximately in the center of the boat? Depends on boat but probably. > dat pic I think you misunderstood the question. When people pull boats along a canal they do it from the path (it's why it's on the picture). There's no tug boat in that scenario. So naturally the rope will be at an angle and hence have a force component towards the canal bank. >> >>15159119 oh fuck holy shit, i thought you are wading in the canal and pulling the boat behind you by hand. i mean who knows, it is such an old book. i was wondering about the meaning of the PATH in that picture but didn't make the connection. so i was filtered by the picture. damn >When people pull boats along a canal they do it from the path never heard of it. that must look funny. >> File: bow hauling.png (356 KB, 530x701) 356 KB PNG >>15159119 found something called bow hauling. here is the setup. >> when deriving the Euler-Lagrange equation we make use of a function $\bar y(x) = y(x) + \varepsilon\eta(x)$. Should $y$ and $\eta$ be of class C2? >> >>15159143 If you are using two ropes that is the best configuration since the torque at the front and back should hopefully cancel. >> >>15159155 What do you mean exactly by class C2? >> >>15159172 the second derivative exists and is continuous >> >>15159176 That is the normal assumption and simplifies the derivation of the equation but I believe it's not a requirement. Though I can't say I've ever seen it derived any other way. Maybe ask /mg/ >> brainlet here. could a higher dimensional person, were such a thing to exist, sidestep "slices" of the 3rd dimension? what i mean by this is that effectively a 3 dimensional person or object can sidestep any 2 dimensional plane by moving in an axis perpendicular to the 2 dimensional planes X and Y. can a hypothetical 4th dimensional or higher person or object essentially just move away at a further perpendicular angle to sidestep a particular slice of 3rd dimension? and i suppose somewhat tangentially, given that any 3D space is essentially made up of an infinite number of 2 dimensional planes, that is, you can move anywhere along the Z axis of a thing and get any number of X and Y planes, could a 4th or higher dimension contain a similar infinite number of slices of 3rd dimensions, geometrically speaking? i am a laymen, im probably not using proper terminology here, and frankly i dont know if i am asking a question or if i just posted 2 paragraphs of garbledy guck, but i appreciate your patience in reading it. thanks >> >>15159323 the answer is yes to all your questions. a higher dimensional person can move along an axis that doesn't exist to a lower one and "jump" locations. e.g. put your finger onto a 2D plane, lift it, and then place it somewhere else. also a 3d object moving though a 2D plane would look like a series of slices to those 2D observers. it's exactly the same when you go to 4D / 3D >> >>15159155 Not really. But usually the Lagrangian forces $q$ to be C^2 so you can calculate $\dfrac{d}{dt} \dfrac{\partial L}{\partial \dot{q}}$, in which case you want everything to be $C^2$ >> Can you induce nuclear subcriticality at the molecular level? My understanding of nuclear reactors is poor, but to my knowledge you can put fissile material in a situation where radiation is reflected back into the material. This promotes further fission, allowing you to "extract" more energy on demand. Is it theoretically possible to do this on a molecular level, say by pushing 2 atoms of uranium close together? Or perhaps a uranium atom against a tungsten atom or whatever serves as a reflector? The reason I ask is that this seems like the most plausible mechanism for bacteria to develop radiotrophy, in a way that doesn't just leech off nuclear waste but actively cleans it. >> >>15159781 > do this on a molecular level, say by pushing 2 atoms of uranium close together? You are essentially describing cold fusion but most scientists say that isn't possible. >> File: 1668319342836452.png (446 KB, 1097x752) 446 KB PNG >>15149490 Good morning /sci/entists! >Why I am asking a question I am working on my book more today. Yesterday a nice anon told me how to make colored boxes. I used bmatrix to put them all into a matrix shape. The end result looks like a matrix, except change digits to colored squares. This works nicely and looks good for small Maid Spaces. I was able to draw a 10 by 10 Maid Space with radix 10 and it looks nice because of the colored squares. However, when I try a bigger one like using a 25 by 25 matrix then compilation fails with errors from bmatrix being too big to typeset. 10 by 10 is fine, so my workaround is just use a smaller one. I think going from counting in a small Maid Space to suddenly showing normal sized PNG images of a Maid Space is too jarring and I want to be able to draw some with more cells. >question Is there a way to adjust the spacing between the squares in a bmatrix to be smaller? I want both the height and width of the whitespace around a square to be reduced so more squares can get drawn in the same page space. Thank you /sci/entists for reading my post. >> File: 1674692611102775.png (389 KB, 600x630) 389 KB PNG >>15159930 Also, I figured out how to put a subscript number after the close bracket of a bmatrix. It is in the bottom right corner. That has the radix. I also want to include the height and width in this notation preferably as a superscript number at the upper left and upper right corners of the bmatrix respectively. Also I want to know how to put a subscript number in the bottom left too. Probably that one will have the number of dimensions of the Maid Space. I want this because I realized I can draw a 3D Maid Space as a series of images on a 2d Maid Space. Maybe I also need some concept of a Maid Frame Counter or something. I don't know. If I get stuck I will ask on a board or just make things up until my Computer Program works. Now every corner has information you need so you have to look at all the corners. This is a good day for doing some Computer Science. >> File: 1671206670043330.gif (864 KB, 640x360) 864 KB GIF >>15159994 Also does anyone think a different matrix would look cooler? I used bmatrix because it looks nice, but there are options and I might switch to a different one or a really super uncommon one or something. Maybe either remove the brackets or change it to double line if I change it. I feel more inclined to remove it than change it because then visual noise is less but at the same time double line looks cool. >> I am using $\texttt{\fontspec}$ but the font I am using does not have oldstyle numerals. How can I import it from another font, which does? >> File: Euler-Lagrange.jpg (243 KB, 780x1372) 243 KB JPG >>15159155 y does not have to be in C^2. It's enough if it's weakly differentiable once. >> >>15158210 thanks >> >>15149490 on average how much time should i spend studying diff eq? is 3 hours per day enough? >> I just took 2 important exams and in both of them I got an A and in both of them the teachers (two different ones) didn't realize that I did a mistake which would have gotten my grade down to a B. Should I take this as a form of encouragement from some higher power? >> File: 167368-Spring-Cat.jpg (76 KB, 480x640) 76 KB JPG Very stupid question, please be gentle. I even LaTex'd it for your convenience. https://mathb.in/74029 >> >>15161081 Line 3 to 4 is nonsense, you just go $\sqrt{a^2} = a$ >> Saved others a click: Say I wish to solve the inequality $|x-1| + |x+1| < 2$. Now, we can make use of the alternative expression for absolute values: $|a| = \sqrt{a^2}$, and what follows is: [eqn]|x-1| + |x+1| < 2\\ \sqrt{(x-1)^2} + \sqrt{(x+1)^2} < 2\\ (x-1)^2 + 2\sqrt{(x-1)^2}\sqrt{(x+1)^2} + (x+1)^2 < 4\\ (x-1)^2 + 2(x-1)(x+1) + (x+1)^2 < 4\\ [x^2-2x+1] + 2[x^2-1] + [x^2+2x+1] <4\\ 4x^2 < 4[/eqn] which reduces to: [eqn](x-1)(x+1) < 0[/eqn] which is true for $x \in (-1,1)$, but clearly it does not satisfy the original question, since the LH side of the inequality above is equal to 2 in this select part of the domain (and it can easily be shown that the statement is altogether false by taking cases). My question is: where (and why) exactly does the algebra fail? >>15161081 You don't know LaTeX works on this board? >> >>15159781 no you still need a free neutron to start the process you'd also need a way of expending enough energy to get the atoms close enough together >> >>15161081 >>15161092 What do you mean? Your answer is correct: $x^2 < 1$, so x = (-1,1) $\pm 1$ are not within that domain >> >>15161112 No it isn't. $|0 - 1| + |0 + 1| = 2 \nless 2$ >> Let E be the field of algebraic complex numbers, and F the field of algebraic real numbers. ("Algebraic" meaning, over the rationals.) Then does F(i) = E ? >> >>15161194 Algebraic numbers are closed under conjugation, so they're closed under taking the real part and the imaginary part. >> >>15161197 Ah got it, thanks >> whats an example of a real function f for which the following is true: -f(0)=0 -f'(x)>=0 on the interval [-a,a], a=/=0 -f''(x)>=0 on the interval [-a,a], a=/=0 -newtons method doesnt converge starting from some b in [-a,a] honestly, i cant even figure out a function that satisfies the first 3 >> >>15161220 >-f'(x)>=0 on the interval [-a,a], a=/=0 >-f''(x)>=0 on the interval [-a,a], a=/=0 sorry, these inequalities should be strict i.e. > (1st and 2nd derivatives are positive on this interval, not just non-negative) >> >>15161179 Just exclude zero? >> >>15161271 let x be in [0,1) then $|x-1|+|x+1|=1-x+1+x=2$ similarly, let x be in (-1,0] then $|x-1|+|x+1|=1+x+1-x=2$ strict inequality does not hold for anything on the entire interval >> File: 1674946007504055.jpg (266 KB, 905x881) 266 KB JPG I refuse to believe that its dangerous to stand under a tree when its lightninging out. The electricity should go through the tree to the ground. Why would it need to go through you when its already in the tree? Is there even actual proof this is dangerous? >> >>15161434 Lightning doesn't have to hit the tree exactly, just to the side...and especially where the gathered ions tell the lightning where to hit. Also, the tree could either explode into pieces upon striking or catch on fire. If anything, find some other shelter that could provide adequate protection. >> >>15149490 Anons who know linear algebra and advanced math, pls help >>>sci/>>15161555 >> >>15161568 Ask your undergraduate advisor numbnuts I don't go to your school 80% of the course description is literally copypasted and it's very basic material, it's probably virtually identical except for 1-2 weeks of tangential extras >> when does geometry, if ever, stop just being algebra? I just don’t get why they’re two separate fields and why geometry isn’t a subset of algebra. >>15161568 Stop worrying it’ll be ez if you study >> >>15160736 Like the calculus kind? 4hrs/term is enough, just to keep in touch with the content. It was just a big of tricks from what I recall >> >>15161220 >>15161223 >honestly, i cant even figure out a function that satisfies the first 3 $x^2 + x$ Basically, you want to do the following: - $f'(x) = 0$ for $x \in (- \infty, b]$, where $b < - a$ - the first step, starting from $a$, has a large enough differential to shoot you to $(- \infty, b]$ What I'd do in your case is look at $f(x) = e^{x^2} - c$ for $x \geq 0$ and $f(x) = -c$ for $x < 0$. >> What do I use this board for? I'm not that into the "sciences" Americans use to refer to when they say "sciences", those being the STEM ones. But where do I go with political science, social sciences, psychology, sexual sciences, etc. Does this also belong here since I want science-founded discussions, does this go to /his/ or to /lit/ if I'm referring to a specific book I've just read? >> $\Phi := \{f \in C^{1}[0,\, 1] \mid |f(0)| \leq 1 \land ||f||_{\infty} \leq 1\}$ I want to show that this set of functions is bounded. Is it enough to explicitly state the supremum and infimum \begin{align} \sup \Phi &= [f: [0,\, 1] \ni x \mapsto x + 1 \in \mathbb{R}],\\ \inf \Phi &= [f: [0,\, 1] \ni x \mapsto -x - 1 \in \mathbb{R}]? \end{align} >> >>15162370 All of these topics belong here. >> >>15162655 I'm assuming the inf-norm bound was supposed to be on the derivative. No. Use mean value. >> >>15162666 not quite, Phi should have been defined like this $\Phi := \{f \in C^{1}[0,\, 1] \mid |f(0)| \leq 1 \land ||f'||_{\infty} \leq 1\}$ Sorry for the inconvenience. How about now? >> >>15162684 ignore, I got what you meant >> >>15161719 thanks man. >It was just a big of tricks from what I recall seems that way so far but im worried its going to get confusing >> Is there a type of seizure that doesn't cause any kind of body movement, instead causes pain in the head rhythmically and with the rhythm of that pain you also hear very loud noises and your vision flashes? >> >>15163014 A migraine. >> File: 1665356345094.png (668 KB, 700x952) 668 KB PNG Let's say I have a large set of matrices. A particular matrix M is an n x m matrix. I'd like to estimate the function f, whose domain is R^m. I can assume that $f(x) = \sum_{i=1}^{m} f_i(x_i)$ and that $f_i(0) = 0$ for any i. For each matrix M, I can direcrly observe the value $F(M) = \sum_{i} f(M_i)$ where M_i is the ith row of the matrix. Given an unseen matrix X along with $\sum_{i} f(X_i)$, I'd like to predict f(X_i) for each row of X. I first thought it was impossible, but I thought about this example - if I have two matrices A and B that are identical (or at least very similar) except at one element $A_{ij} \neq B_{ij}$, then $F(A) - F(B) = f_j(A_{ij}) - f_j(B_{ij})$. If $A_{ij}$ or $B_{ij}$ happen to be 0, then I know the value of $f_j$ at the nonzero one. Realistically, I doubt there are many instances of matrix pairs that are equal except for just one element, but there might be a good amount of pairs that are very similar. This makes me think there is some way to approximate f with some statistical model and smart math. Is there such a way? >> Can isolated systems truly ever exist in the real world? >> I know that every irrational has a sequence of rationals approaching it, but can we pick a series of rationals that monotonically increase to any irrational? >> >>15163125 No, but you can make them isolated enough to be fit for purpose. >> let us sing a prayer for calc chad >> >>15163125 if by "isolated" you mean "closed", then the universe is by definition an isolated system. >> >>15163279 Not true since the universe is expanding. >> >>15163427 i dont see how that refutes my claim >> >>15163427 That doesn't change anything. >> >>15163430 >>15163432 Because energy is no longer conserved. >> >>15163435 first google link https://www.futurelearn.com/info/courses/mysteries-of-the-universe/0/steps/212125 >The question about energy conservation in an expanding Universe is one instance of how our knowledge of modern physics start to get challenged as we explore more extreme environments and distances. And the answer to this question is: there is no violation of energy conservation during expansion of the Universe. >> >>15163443 second google link https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/ > Energy isn’t conserved; it changes because spacetime does. >> >>15163447 third google link https://physics.stackexchange.com/questions/259759/conservation-of-energy-vs-expansion-of-space >Some people claim incorrectly that energy is not conserved in an expanding universe because space-time is not static. The law of Energy conservation is derived from Noether's theorem when the dynamical equations are unchanged with time. These people confuse the invariance of the equations with the invariance of the solution. Space-time changes but the equations obeyed by the expanding universe do not change. Space-time cannot be treated as a background, its dynamics must be included when deriving the enrgy equations via Noether's theorem. This leads to the equations given above which show that energy is indeed conserved. >> >>15163451 Who should you believe, some random poster or an article from an actual theoretical physicist? *shrug* >> >>15163457 i dont have to "believe" anything, i have eyes and i can read arguments. my link is very clearly a direct refutation of yours. also, my physics professor once told me that the entropy of a closed system never increases, so fuck physicists. >> >>15163465 > the entropy of a closed system never increases it doesn't, for some particular definition of a system. >> >>15163471 i refuse to be gaslit on that particular matter any further. >> Can you tell the sex of a person based on any single cell extracted from their body? >> >>15163846 Yes if you exclude intersex. >> >>15163846 yes. DNA tells you the gender of the organism the cell came from. >> >>15149490 I have a few questions about different types of amphetamine salts. I really dislike methamphetamine but enjoy dextroamphetamine because it makes me get up and do stuff. Why is this? Just the difference between pharmaceuticals and street drugs? Or is it chemical structure? I have been diagnosed with Schizophrenia (Paranoid) as early as 18 years old. At times, occasional methamphetamine use made me super paranoid, recklessly impulsive, as well as have some delusions and confabulations. But I've been taking some doses of dextroamphetamine (25mg a day across 5-10 mg doses). It has given me a great sense of productivity and made me actually live my room, clean the kitchen and my room, as well as make me generally more active. I won't take it often because I know it's highly addictive, and it's expensive to get without a prescription, where psychiatrists won't usually give it to schizophrenics anyway. I guess the dosages would affect me differently, too, but I never took meth too frequently nor too much (although I usually smoked or drank it alcohol). >Dexies Pill form. I have experienced significant appetite suppression, increased concentration, some considerable irritation when reading something I disagree with, as well as more energy and less fatigue (I walked and brought 17 hardback books in two bags back to the library, which I might have found too tiring usually as someone with avolition). I had increased sexual pleasure but not really as much horniness. I did take it first with LSD so it might have been impacted by that, but it generally made me love music more, as well as feel energised. Sadly, it did cause me to go back into insomnia, though I was able to sleep 8+ hours recently once I came down. >Meth Horniness to the point of being uncomfortable, making up memories and weird shit, intrusive thoughts, general psychotic symptoms, some euphoria but also a lot of disinhibition, agitation. >> Good Morning /Sci/entists. >What I am doing I am working on the Maid Space book more. I am typesetting a Maid Space by using bmatrix. Doing this\begin{bmatrix}
\square & \square \\
\square & \square
\end{bmatrix}_{2}^{(2, 2)}$This would make a 2 by 2 Coolkyousinnjya Maid Space Zero with the subscript 2 in the right corner to let you know it is radix 2 and the (2, 2) superscripted into the top to tell you it has height 2 and width 2. >question How do I put a subscript and superscript number on the left corners of bmatrix? >Why I want this I was looking in the Wolfy book about her triangle experiments. She had one-dimension dot-lines and made up rules that cause the dots to change position or increase or decrease the number of dots on the dot-line. If you get a dot-line and apply a rule to it and get a new dot-line and do that a lot of times, and you put the dot-lines on top of eachother, then you end up with a 2D drawing that shows that actually those dots were drawing triangles, but you can't see the triangles until you put all the lines together and draw it in time order. Similarly I figured out I can do the same trick with a 2D Maid Space and can represent a 3D one as a lot of 2D ones. If you want to imagine this mentally think about how a flip-book animation works. I want to put the Maid Frame Count at the top left of of the bmatrix. I will figure out something else to put in the bottom left so every corner gets a number and it makes it look cool. >bonus question What looks the coolest if you fill it with colored squares and put numbers on all the corners? matrix, pmatrix, bmatrix, vmatrix or Vmatrix? Thank you /sci/entists for reading my post. >> >>15161581 >>15161717 Thanks frens. My advisor recommended that I take LA and Stats for engineers. Will try to cover the material before the semester starts to get ahead. Thanks for replying in /mg/ as well. appreciate the advice/ >> >>15164407 Tried Tensor. Didn't work. >> File: Not leaving.png (794 KB, 644x900) 794 KB PNG >>15164467 Reread the Tensor example. I was using it wrong. Tensor was the answer. Tensor will protect you from the terrible secret of Space. Space has a terrible power. Do you have stairs in your house? Please go stand by the stairs. Now it looks how I want and I just have to figure out what goes in the bottom left corner. I might change it where upper left has Current Maid Frame Count and lower left has Total Number of Frames and upper right has coordinates and lower right has radix. That way it has everything needed to tell you got all the information and you can see how to read it and how to order it and look more at the squares for patterns of squares that have data in a big number. Then I can have Four Corner Maid Frame Maid Address Notation for Maid Space. Then nobody can ever tell me a maid isn't related to science or math ever again and I can go in a science meeting and somebody will let me talk with PowerPoint and I get a science lunch where it is a white box that has a turkey sandwich, a random Lay's product, and a random can of soda. Sometimes a charcuterie board with little cheese cubes and some kind of pepperoni. I am going eat that lunch and look at birds and use my computer outside and give the birds some of whatever the Lay's product as long as it isn't flamin' hot. Then later I get a science foundation in new mexico and my assistant has huge boobs and wears a maid dress and dra/g/on horns at all times. Her job is being a maid who follows me around and takes notes when people tell me things so I don't have to do it and later I know what was said because the maid wrote it down for me. Her other job duty is use the coffee machine to make coffee. She also helps you find where things are in large buildings because navigating a building is a confusing task and it is easy to get stuck in a loop where you keep arriving at the same waterfountain somehow or the stairs didn't get changes when you used them. Every scientist will have a maid who does this. >> File: Programmirovanie.jpg (45 KB, 200x340) 45 KB JPG does anyone have a copy of pic related? >> >>15149490 I'm looking at the divergence formula for an electric field in spherical co-ordinates, and it includes redundant terms that cancel out. Why are they there? >> $\sqrt{\mathbb{R}}=\mathbb{Q}?$ >> >>15164852 The right - side terms are within that differentiation operator, they aren't coefficients like the ones in the demoninator. >> File: shane-panel.jpg (41 KB, 400x367) 41 KB JPG freshman in an integrated master's program for physics here I'm interested in cs-related stuff (programming, linux, cryptography, etc.) so I'm guessing quantum computing will be an interesting and useful topic to learn? What kind of prerequisites should I have and what kind of books should I read? I'm planning to start reading Shankar after I finish Morin's classical mechanics book (which I should be done with in like 2 months, only have ~30% of the book left). Unrel but is it worth reading L&L for classical mechanics (or anything else)? I'm planning to read Goldstein in the future. >> Why does my professor insists in calling this thing a "Lorentzian"? $\hat \alpha(\omega)= \frac{e^2}{m} \frac{1}{(\omega_0^2 - \omega^2) - \mathrm i \omega/\tau}$ From wikipedia, it should be something like this: $f(x; x_0,\gamma,I) = I \left[ { \gamma^2 \over (x - x_0)^2 + \gamma^2 } \right]$ And I can't really map one on top of the other. >> Anyone know of good books for learning about piezoelectricity? >> >>15149490 If three dimensions is a box and two dimensions is a square and one dimension is a line, then is zero dimensions a point? What is negative one dimensions? Negative two? Seventeen dimensions? What are they and how do they get drawn? Is Yachie a turtle? If not, why does her tail come out of the back of her head? >> >>15164909 For L&L, I like it. If you already know some physics, it is a good second course. >> >>15165758 Yes, 0D is a point. In this sense, for the geometry of an object, negative dimensions obviously do not exist. A different definition could be generalized to negative dimensions, but you won't draw a box in -2D. https://math.stackexchange.com/questions/100883/has-the-notion-of-having-a-complex-amount-of-dimensions-ever-been-described-and >Is Yachie a turtle? Is that not a dragon tail? I think it just comes out of the shell on her back. >> >>15165758 have some vids for 4d https://www.youtube.com/watch?v=by8eAnez0i8 https://www.youtube.com/watch?v=1ad9y0FmQ9g https://www.youtube.com/watch?v=POzuXyuF9DQ https://www.youtube.com/watch?v=dbq9uX_MycY >> File: yachie.png (15 KB, 1154x130) 15 KB PNG >>15165758 >> >>15165816 Thank you for telling me. The way I was imagining it a 0 dimension Maid Space has one digit. If you give them an index for time with the Maid Frame Counter then you can put the 0 dimension Maid Spaces next to eachother based on that time order and get a Maid Time Line. Then you can put all the Maid Time Lines together and get a Maid Time Rectangle. Then you can put all the Maid Time Rectangles together and get a Maid Time Cube. I don't know what shape you get when you put all the Maid Time Cubes together, but it can I guess be thought of as a 3D Maid Space that changes with time? I don't know even how to consider more than four because somehow time has to have a shape first and I don't know how even to consider dimensions bigger than four. I couldn't really tell it is supposed to be a shell because the color scheme for the tail to too similar. There also aren't many Yachies I have. I didn't know this character existed but someone made a thread with a huge boobs Yachie who sort of resembled Tohru, and Touhou was in the file name so I think maybe Yachie is the big titty dra/g/on maid I am hoping for. Upon closer inspection, I discovered that I can find Maid Yachie or huge boobs Yachie, but not both at the same time. Also there are only a very small amount of Yachie drawing where she has a maid dress. >>15165924 Thank you for sharing videos. >>15165927 Thank you for telling me. If Yachie has a dragon tail and horn then I think she qualifies as a dra/g/on maid. >> File: 1672366750533.png (46 KB, 970x470) 46 KB PNG I'm sleep deprived What compound is this >> The planets all revolve around the sun on virtually the same plane of eccentrcitiy right? And the moons orbit their planets on that same plane as well? That can't be a coincidence. If gravity and space and forces and shit all work in 3 dimensions, why does nothing orbit around the sun in relatively vertical plane? Likewise galaxies are really flat, why not spherical? >> Why do British people put an 's' on math? Sounds so retarded >> File: 1671959187346.png (441 KB, 1600x1133) 441 KB PNG >>15166793 I think they do this because there is more than one of them? Also is the ice maid smart? I see her doing advanced math a lot of times. >> >>15166848 there is more than one art but we dont say arts when referring to the topic of art in general. the s on maths is retarded >> File: 1669394574680729.png (202 KB, 655x748) 202 KB PNG >>15166855 It is maths. Do the math, do the math, do the ma Unintelligent error from Americans probs due to obesity. >> >>15166857 only a brit would be so obsessed with america and sticking to bad grammar. i could understand if you all used the singular form of tooth rather than teeth, because that would be accurate for you all >> File: 1647298496107.gif (322 KB, 370x330) 322 KB GIF >>15166765 I seriously need help here, is it a 1-butanol? isopropyl alcohol? cyclohexanol? That C-H stretch is seriously fucking me up >> >>15166879 short of matching it to a known spectrum like a fingerprint, I don't think you can reasonably tell. It's an alkyl alcohol, that's it. >> >>15166898 It's supposed to be C4H10O, I just don't know the structure. In the NMR there is a triplet at 0.9 ppm and another at 3.5 ppm Then there is a clusterfuck going on somewhere in 1.5 ppm I thought it was 1-butanol since yesterday but now I'm not so sure. ChemDraw prediction for it seems close enough though >> Do virtual photons exist? >> >>15166908 >triplet at 3.5ppm CH's near an alcohol and two neighboring H's >triplet at 0.9ppm CH's with two neighboring H's, not anywhere near a heteroatom >clusterfuck around 1.5ppm CH's around multiple distinct carbon centers cmon anon, put the pieces together. What about integrations? >> >>15167156 >integrations 0.94, 3. 1.3, 2. 1.5, 2. 3.5, 2. It's just 1-butanol, I'm so stupid. >> What has higher chances of being automated, being a data scientist or a pure math researcher? >> File: Capture.png (2 KB, 274x53) 2 KB PNG can anyone get me started on this diff eq? (using homogenous method) >> >>15166790 The orbiting bodies are attracted to each other as well as the star which naturally brings them all to their average or center of mass (in the z plane) while their orbit and motions in the other directions are dominated by the star. >> why isn't there a single good /sci/ archive? >archived.moe, fireden no search >warosu total dogshit in every aspect, only thing for it is that it has zero competitors >wakarimasen dead (formerly good) >desuarchive, 4plebs don't cover /sci/ why did fireden disable search? Used to be better than wakarimasen since fireden archives were older than wakarimasen's. And why has archived.moe disabled search? /sci/ is an important board, how is fucking /d/ so much better off than us? >> >>15168093 only thing going for it* >> File: 1669752282000229.jpg (174 KB, 1074x800) 174 KB JPG >>15164909 halp need to into cs stuff as that seems to be the best way to make bank while still doing something i'm interested in >> >>15166793 It is just a question of habit anon, 'math' sounded silly to me at first, but I quickly got used to it. It does not really matter. I guess it is because even americans say 'mathematics' in the plural. >> File: proxy-image (2).png (419 KB, 1024x644) 419 KB PNG does anyone know how I might contextualize reagent testing in a general like math way? for example I want to write a program where you input a series of test result colors (of any length, and these results would probably be a tuple with the test used- [color,test]) and output a list of possible substances. optionally too, an easy way, if the output list is >1, for it to project from there all possible [color,test] series that would result in the most specific substance possibilities. (so like if an output list is A,B,C,D and substances C and D are not differentiable with any testing, it would give something like { [test1,orange],[test2,blue],A; [test1,orange],[test2,blue],[test3,blue],B; [test4,red],C,D } ) I'm using the word series, but I guess order doesn't matter right. I don't remember much of this kind of thing. >> >>15168093 Any particular issues with eientei.xyz? >> >>15163996 jerking off on meth is something else. something forbidden to mortals. I'm not fucking around, don't ever do it. >> File: proxy-image (3).png (281 KB, 448x222) 281 KB PNG >>15165758 read these they're fun >> (Not a question) I'm learning calculus and using Khan Academy for practice problems. >A particle moves along the x-axis. The function $x(t)$ gives the particle's position at any time $t≥0$ >$x(t)=t^3-3t^2+7t-6$ >What is the particle's acceleration $a(t)$ at t=3? I made no mistakes in my calculation but I submitted the wrong answer because I submitted the first derivative and it was never mentioned that acceleration is the derivative of velocity. >> what courses should i complete on khanacademy before attempting to get my ged? >> >>15168093 >/sci/ is an important board, lmao >> >>15165304 squish material -> get voltage apply voltage -> squish material saved you$150
>>
How the fuck do I solve i·z^3-27=0?
>>
>>15169041
no differently than you would solve any similar equation
iz^3=27
z^3=-27i
take the cube root of both sides and simplify
>>
how do I show that a set of functions is closed? Any suggestions?
>>
[eqn]
|729.000000|^{1/(2 * 3)} \cdot e^{i(-1.570796 + 0\pi)/3}\\
|729.000000|^{1/(2 * 3)} \cdot e^{i(-1.570796 + 2\pi)/3}\\
|729.000000|^{1/(2 * 3)} \cdot e^{i(-1.570796 + 4\pi)/3}\\
[/eqn]

Rule of thumb: Use polar coordinates for multiplicative problems. For additive problems, go with the a + bi form of complex numbers.
>>
>>15169234
>>15169041
>>
File: beakus_amogus.jpg (52 KB, 604x680)
52 KB JPG
>>15149774
Define "hate" and define "math".. I've had a prof that went full symbolschizo which is acceptable with experience but not to beginners, and used ms paint to draw symbols rather than put in some effort into learning latex. And it was all done through zoom so good luck finding shit. Students didn't like it and I bet no mathematician would enjoy it either.
>>
Anybody here happen to know WTF a fixed rotation is in classical mechanics? My teacher keeps talking about free rotations, free-fixed rotations, etc. but I just cannot find out what it means when a rotation is fixed.
>>
>>15169672
Why don't you ask her what she means by a fixed rotation?

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