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/sci/ - Science & Math

You cannot reply anymore.

Formerly >>14843727

>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 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

>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
>charts?
imgur.com/a/pHfMGwE
imgur.com/a/ZZDVNk1
>tables, properties and material selection?
www.engineeringtoolbox.com
www.matweb.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
>>
How do I create Chad offspring without being a Chad myself? Can it work like this?
>>
>>14858868
Sperm clinic, or be the betabuxx of a woman who got pumped and dumped by Chad.
>>
Suppose $n_1 +\cdots + n_k = N$, $n_i\in \mathbb{N^+}$.
It is well known that the number of $n_i\geq1$ (i.e $k$) is $O(\sqrt{N})$.
Now I read here that more generally there are $O\left(\frac{\sqrt{N}}{2^t}\right)$ number of $i$'s such that $n_i\geq2^t$ but I can't prove it. (Also there is a chance this fact is wrong).

I've tried bounding the count ($C$) like this $2^t + (2^t+1) + \cdots + (2^t+C-1) \leq N$ but I can't reach the $O\left(\frac{\sqrt{N}}{2^t}\right)$.

Any ideas? Can anyone prove/disprove it?
>>
>>14858719
Someone please explain to me what even the point is of all these thermodynamic potentials? (Like Helmholtz, Gibbs, etc.) And how tf do you get them and how tf do you know if a variable is fixed and when can you fix them?
>>
>>14858904
Actually there might be a typo, the Japanese translation apparently has the bound written like $O\left(\sqrt{\frac{N}{2^t}}\right)$, I still can't prove it though.
>>
Is transitivity the most important property for an ordering?
>>
>>14858868
>>
>>14859178
for me it's antisymmetry.
>>
>>14858904
The problem makes little sense from what I see here. What's stopping you from selecting $n_1 = N$ for every $N$?
Then of course $k=1$ which is $\Theta(1)$.
>>
>>14859210
what about $>$
>>
>>14859314
First of all I am just given the numbers and want to find a bound.
Second of all I am really stupid because I didn't clarify it in the original post:
>>14858904
>>14858907
All $n_i$ should be distinct.
>>
>>14858868
Test creams, those stick in your skin
>>
>>14858904
>>14858910
Have you tried writing out the closed expression for $2^t + (2^t + 1) + \ldots + (2^t + C - 1)$?
>>
>>14859354
yeah and I solved the quadradic. I didn't achieve the bound, maybe I am doing the calculations wrong. ($C\cdot2^t + (C-1)C/2 \leq N$)
>>
>>14859357
Divide both sides by $2^t$.
For $N$ sufficiently large you can assume that the largest possible value on the left is assumed with $(C - 1)C/2^{t + 1} \geq C$, so for Landau notation purposes you can discard the $C 2^t$ term then square root both sides.
>>
>>14859386
I don't really follow. Could you write down the equations (no need to explain the steps I just want to see them)?
>>
>>14859421
Nvm, I think I fucked up.
>>
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What is the upside down triangle by C4 supposed to represent? TP14 is a test point where you feed in an RF signal. Maybe a reference voltage?
>>
Sup /sci/bros
I just transferred to a CS BS program from community college.
I was wonder what should I do to stay ahead or even fill gaps?
I studied a lot of math but wanted to do something more applied after my proofs class.
>>
I an studying chemistry in school. I love the problem solving and working with the theories and abstract concepts to solve problems, but as soon as I enter into a lab or have to deal with the "messiness" or real scenarios my interest wanes significantly. Is there something else that I can study that is more working with abstract concepts to problem solve? Will I enjoy computer science? Will it provide me with career opportunities where I can have minimal contact with other people?
>>
>>14860736
You can't get a good job with theory.
Just pick up a book and study theory as a hobby
>>
>>14860284
>What is the upside down triangle
antenna
>>
>>14860736
Physics is the closest to chemistry that it also theoretical.
>>
>>14860736
>Will it provide me with career opportunities where I can have minimal contact with other people?
Unfortunately, no. That might have been the case 20 years ago but nowadays there's daily standups, weekly meetings with your manager, team meetings, code reviews, etc, and dozen other bullshit meetings per week that you're supposed to attend. Plus the expectation to socialize during lunch and after work. It's just another normie bullshit office job now. It's entirely possible to fill up your schedule with so much crap if you want that you don't even need to program and if anything your performance reviews will be even higher because you participated in meetings.
>>
Q: What caused my wall outlet to shoot the ungrounded device's plug 6 feet away when i turned said device on? The outlet had char marks after, too.
>beyond lost trying to look this up, everything is about motors or weak forces
>all i can remotely estimate is electrostatic discharge or induction
I just want to know how electricity can make something move that far that fast, without a damn motor.
>>
>>14861013
>Q: What caused my wall outlet to shoot the ungrounded device's plug 6 feet away when i turned said device on? The outlet had char marks after, too.
Localised heating vaporising something resulting in propulsion due to gas pressure. It's possible that the Lorenz force was also a factor, i.e. a brief spike of extreme current turning the plug into a railgun. But vaporisation seems more likely; if the socket is an enclosed space with very little volume, you wouldn't need much gas to create a significant pressure.
>>
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>>14858719
Why does sodium only like yellow?
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>>14861066
I should have specified that I believe it was a 240v outlet, 120v device, as the area used to be a workshop in the 40s. I hadn't known those wires were 240v. The device was fine, worked still.

But thanks. I believe those two possibilities should be enough to research further and quell my decade long mystery I think of now and then but never asked why.
>>
>>14861070
it doesn't just "like yellow," but those are the strongest absorption lines for sodium atoms.
the excitation of the ground state 3S electron to either the 3P1/2 or 3P3/2 is at 589.76 nm and 589.15 nm, respectively. These are both yellow wavelengths.
There are other transitions, but their relative intensities are orders of magnitude lower and they are in the ultraviolet (or not originating from the ground state)
>>
>>14861153
What happens to the sodium electrons if exposed to uv?
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>>14861174
I'm going to guess it goes to 3s2
>>
i might just be retarded but can multi linear maps be represented as matrices within matrices?
>>
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>>14858719
could use help with this. not really sure how to build an equation using those variables
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>>14858868
expose your kids to activities as much as possible (karate, diving lessons, rock climbing, archery. chess)
>>
>>14861242
use faradays law to get the magnetic field and then the one that connects flux with the rate of change of something (forgot the equation xd)

maybe someone else can help you more, i could but then i'd have to refresh some shit
>>
>>14861177
S has only one orbital dummy
>>
>>14861223
Yes, I don't see why not as long as they vector spaces involved are finite dimensional.
Using currying you can view a multilinear map $V_1 \times V_2 \to W$ as an element of $\text{Hom}(V_2, \text{Hom}(V_1,W))$.
Each element of $\text{Hom}(V_1,W)$ can be represented as a matrix so any element of $\text{Hom}(V_2, \text{Hom}(V_1,W))$ can be viewed as a matrix whose entries are matrices.
Same if you have multilinear map $V_1 \times \ldots \times V_n \to W$. Then you can view them as elements of $\text{Hom}(V_n, \text{Hom}(V_{n-1}, \ldots ))$ and you will get matrices within matrices within matrices within matrices and so on.
>>
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Is the fact that so much information is collected from us evidence that this could be a simulation? Is it pure coincidence the we happen to live in the perfect point of time where data gathering makes simulation possible? Why do we experience this particular point of time and not the dark ages where almost no information was left behind for computers to process it?
>>
/sci/ I have a dumb question.

If a wooden arrow with an iron point was shot from a bow, and the wooden shaft was incinerated mid air, leaving only the iron part flying. Would it still have enough force to do harm to a person without an armor? Or what would have happened to the iron bit, would it fall flat?

I am oblivious to rules of physics, so have no clue.
>>
>>14861374
The amount of damage it can cause comes from its kinetic energy. So if half the total mass of the arrow is in the shaft and that disappears then the remaining arrow will cause half the damage.

However losing the shaft and tail feathers will drastically affect its aerodynamic properties. Both those things help to keep the arrow stable and on course. So the arrow head might start spinning and no longer strike point first, and even then not in the place it was originally aimed at.
>>
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How would I solve this?
What I did is, plug in z=x+iy
Solve accordingly, separate the real part from the imaginary part
The imaginary part (which in my calculations is a fraction, 4y/((x+2)2+y2), sorry I don't know latex) equal to 0
And then what, y=0 with x≠-2? Does this even make any sense?
>>
>>14859050
answer my stupid question
>>
In Stein's gate episode 7, Okabe sends a text message to the past with winning lottery numbers and creates a new timeline. In this new timeline, only Okabe remembers sending the text as they haven't sent it yet in that timeline. the shrine femboy had bought a lottery ticket because Okabe had told him to. But Okabe never actually sends a message through the time machine in this timeline. How come?
>>
>>14862023
First define what $I_m[/math is. >> >>14862055 the imaginary part of a complex number, in the case of z=a+ib it's b >> >>14862023 If z is a real number then (z-2)/(z+2) is also a real number because R is closed under the basic arithmetic operations (provided that the denominator isn't zero so z≠-2), so yeah you already solved your problem, i don't see what else you want. >> >>14862073 I don't get it, z is a complex number, not a real number, x (or a) is its imaginary part You're saying that my calculations are correct and y (or b, the imaginary part of z) can only be 0, therefore making z a real number? >> >>14862023 Right method but I think your fraction is wrong. [math]Im \left( \dfrac{z-2}{z+2} \right) = Im \left( \dfrac{(a-2) + bi}{(a+2) + bi} \right) = Im \left( \dfrac{((a-2) + bi)((a+2) - bi)}{(a+2)^2 + b^2} \right) \\ = Im \left( \dfrac{a^2 + b^2 - 4 - 4bi}{(a+2)^2 + b^2} \right) = \dfrac{-4bi}{(a+2)^2 + b^2}$

So

$\dfrac{-4bi}{(a+2)^2 + b^2} = 0 \implies b = 0$, therefore $Im \left( \dfrac{z-2}{z+2} \right) = 0$
>>
>>14862065
Ok then
[eqn]
\frac{z-2}{z+2} = \frac{z-2}{z+2} \frac{\bar z + 2}{\bar z + 2} = \frac{|z|^2 + 4 i \Im(z) - 4}{|z|^2 + 4 \Re(z) + 4}
[/eqn]
So
[eqn]\Im \left( \frac{z-2}{z+2} \right) = \frac{4 \Im(z)}{|z|^2 + 4 \Re(z) + 4} = \frac{4 y}{x^2 + y^2 + 4 x + 4}[/eqn]
>>
>>14862093
>>14862084
alright thank u guys
>>
I think I'm gonna die. Recently I've been feeling my heart racing out nowhere and then it becomes hard to breathe. Am I fucked?
>>
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How would I define this "curve" as a function? I know there are like those combined function things where you do like:
>f(x) =
> { 0 < x < 3 }
> { 3 < x < 6 }
but I'm not really sure how to form it correctly since it repeats... Also can those combined functions be turned into a single function, or do the a < b < c conditions prevent that from being possible?
>>
>>14862146
f(x)
= x | 0≤x<3
= 6-x | 3≤x<6
= f(x-6x/6) | otherwise

Or you can replace the last case with:
= f(x+6) | x<0
= f(x-6) | x≥6

Or omit the last case and add f(x+6)=f(x) separately, which implies that it's periodic with period 6.
>>
>>14862240
>= f(x-6x/6) | otherwise
That should have read
= f(x-6[x/6]) | otherwise
where [...] is the floor symbol (which 4chan eats).
>>
>>14862240
>>14862243
could you do it with like, a sine function as well? The shape is pretty similar but it's like really flattened, taking it to a limit in some way maybe?
>>
Anyone have advice for writing a manuscript? I've never done one before and I'm struggling to extend the word count out
>>
How do you stay focused when writing long documents? I’ve been working on a monster for a few months now, I’m up to 170 pages, and I’m rapidly losing interest in the thing because I’m almost 100% sure no one will ever read it.
>>
>>14862281
>>14862146
>>
>>14862332
There is +3 at the end
>>
>>14862327
If you’ve said all you need to say, extending the word count out is pointless.
>>
If you’re taking the log of a dataset to better compare small and large numbers, is it better to do log10 or ln? Does it really matter?
>>
>>14862332
>>14862337
neat
another dumb question, but is it possible to invert this to solve for x, given some y? I've never done algebra with a floor in it before...
>>
>>14862365
log10 is more intuitive because it's basically just the number of digits.
>>14862031
I don't think anything in particular would happen.
>>
>>14862281
You could use the Fourier transform to express the function as a sum of an infinite number of sines. You could also use arcsin(sin(x)) or arctan(tan(x)) etc (with scale and shift on input and output), but that's sort of cheating.

Piecewise functions generally can be written in terms of abs(), min(), max() or the unit (Heaviside) step function, and any of those can be approximated by a smooth function; e.g. abs(x) ~= sqrt(x^2+k^2), with smaller values of k producing a sharper "corner" at 0 (k=0 is literally abs(x) = sqrt(x^2)).

>>14862366
You have to restrict the range to half a period for the function to be invertible. In that case, it's just y=x <=> x=y. Otherwise there are infinitely many x for any given y.
>>
>>14861174
certain UV wavelengths send the 3S electron to 3D, 4P, 4D, or higher orbitals. That happens around ~300 nm for these three, and then it only gets lower from there for higher states before you eventually ionize the electron.
>>
stupid question. why does my lamp have 4 positions? on, on, off, and off? why not on and off?
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How do i do rule of inference Simplification without using it?

I am trying to prove the conclusion p -> q and i have worked down the hypothesis to:
~r & (~p v q)

I know i have (~p v q) becomes (p -> q) but i want to get rid of r on my own without invoking the rule of inference.

would i do something like this where i introduce my own axiom thing?

~r & (~p v q) & T

i've never introduced anything before like this so im not sure what to do from T.

would i do something like using T like T = (~r v r)?
>>
x^(2)+2x+x^(5)-2√(x)
Is this a polinomy?
>>
What are some good resources to get better at intermediate algebra? I know its embarrassing to be doing intermediate algebra in college but I fucking suck at graphing. Khan acacemy doesn't really have the specific types of problems I need. I just want to be less stupid man. My biggest problem with all math teachers is that they kind of just "do it" rather than teach it hands on. I need help.
>>
I need to invert the function $y=\frac{ \mathrm{sec}(x) - 1}{x}$ over $0 < x < \pi$. $0 < y < \infty$.
I could just resort to numerical approximation (notwithstanding sensitivity issues) for each input $y$, but is there a better way to get what I want? Like a closed-form expression for $x$ in terms of Bessel functions or something.
>>
>>14862836
If you can't find any examples that are simple or complex enough for you, look through a problem set in a textbook and try to modify it until you finally "see" what you expect to see.
Also, practicing drawing (as in, drawing spheres, fruits, or shells) can help with graphing in general.
>>
>>14863118
I really want online examples, im not smart enough to activity know how to make shapes. I wish I can turn off the autism in my head and be smart.
>>
>>14862366
It is not one to one, so there are infinitely many solutions for inverses like trigonometric ones, but with a period of 6.
>>
>>14862531
arcsin (sin x), wtf shouldn't it be equal to just x??
>>
>>14863340
No, why the fuck would you think this? If this were true you would get
[eqn]x + 2 \pi = \arcsin( \sin(x + 2 \pi)) = \arcsin ( \sin(x)) = x \\
2 \pi = 0[/eqn]

A non-injective function like the sine function can't have a left-inverse.
>>
>>14863347
>No, why the fuck would you think this
It's pretty obvious why he would think this. Are you retarded?

>>14863340
It is but only for $|x| \leq \pi/2$. However, $\sin \circ \arcsin x$ is always $x$ in $\mathbb R$, but that's not saying much because the domain is $[-1,1]$
>>
>>14863340
sin() isn't injective; for any given x∈[-1,1], there are multiple y such that sin(y)=x. Conventionally, arcsin(x) is the value in [-π/2,π/2] whose sine is x.

sin(x+2nπ)=sin(x) and sin(π-x)=sin(x).

If you plot arcsin(sin(x)), you get a triangle waveform.
>>
How do I read this?
>>
>>14863655
$f \text{ maps positive integers to itself, and nonpositive ones to 2 subtracted from itself}$
>>
>>14863674
ok thanks
>>
>>14863674
like this?
{...6, 5, 4, 3, 2, 1, 0-2=-2, -1-2=-3, -2-2=-4...}
{...6, 5, 4, 3, 2, 1,-2,-3, -4...}
>>
>>14863758
Like this actually:
$\{ \dots(-2,-4),(-1,-3),(0,-2),(1,1),(2,2),(3,3) \dots \}$
>>
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>>14858719
Can any mycologist tell me what species this is? Is there any chance that it's poisonous? Does it look like a psilocybin-containing species?
>>
>>14862825
I don't understand the question, are you trying to prove p -> q from ~r & (~p v q) ? Because that seems obvious
>>
>>14864175
I could not get any spores out of it and it does not appear to have a bruising colour. I have consumed an infusion made with a small piece of it in boiling water. I do not feel anything so far (consumed about 10 minutes ago).
>>
>>14864301
You're boiling and consuming a mushroom within 40 minutes of asking whether it's poisonous before getting an answer?
>>
>>14864814
If no one's gonna tell me I have to find out for myself. I haven't had any more yet. Planning on having a larger portion tomorrow if I don't have any negative signs within that 24 hour time period. I'm pretty sure it is of genus either Psilocybe or Panaeolus, just not 100% certain.
>>
Can anyone tell me what the short circuit current would be if you shorted it across ab?
>>
>>14864881
6.62 A approximately
>>
>>14858719
Would a fourier transform or wavelet transform be better for characterizing the sound of tapping on different surfaces? I'm trying to train a machine learning model to identify different tapping sounds. So far I've used a canned FFT function on raw audio data and have been able to train one to tell a desk tap from a keyboard key press almost every time. Although taps on similar sounding surfaces have proven more difficult. Would wavelets be better? I know fourier transforms
>>
if you are given the location of an object as r(t) and the equation of a plane. how would you find the location and velocity of that object when it hits the plane?
>>
>>14865119
I got 6.4 Did I miss something with his ix?
>>
>>14865119
>>14865235
Thanks bros. Mind telling me what method you used?
>>
will i ever stop smelling body odor in college
>>
Math anons, should I take discreet math before Linear Algebra? It's not compulsory, but some of my friends told me that it'll make LA easier.
>>
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>>14858719
Honestly, is it worth it to become an engineer later in life?

I'm a 31 y/o biotech patent examiner but I sincerely wish I'd become an aerospace engineer.

What do? Too late?

Current plan is:

1) Take requisite calculus/physics/engineering at CC until I meet transfer requirements for the local state school (Purdue) while working my job and saving money.

2) Transfer to full time undergrad for MechE with a focus in aerospace courses as I've read that is more flexible. Frankly if I'm changing profession anyway I'd also consider CivE so I could converse directly with concrete and work outside sometimes.
>>
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>>14858719
>>14858734
>>14858872
yeah

https://satanslibrary.org/English/Torah_and_the_Jews_Exposed.pdf
>>
>>14865650
I think you should take discrete math as soon as possible. Really focus on that class (most especially if it is proof based). Focus on logic, set theory and proof techniques. Practice doing proof exercises in your book over and over until you really understand them. Focus on definitions of fundamental things (like relations, functions, operations, etc). A lot of math will be made easier by "unpacking" what you're given in the hypothesis of the things youre trying to prove(most theorems are of the form "if p then q"). It will also help when setting up regions to integrate over when you get to calculus 3, setting up probability problems, and of course linear algebra proofs. Best of luck to you anon.
>>
>>14865210
It's been a while since I've done anything like this but couldn't you set r(t) equal to the equation of a plane and then solve for t, then plug that t into either r(t) or the equation of the plane? IIRC you can express a plane in three different ways (dot product with the tangent vector set equal to 0, and a couple others) so you may have some work to do there. anyway then to find velocity you just use the fact that velocity is the derivative of position. so find d/dt[r(t)] to get the derivative function of r and plug t into that
>>
How do I cope after failing a class I was sure that I was going to get a good score in? I am trying but I can't even get out of the bed.
>>
Two college friends were bad at programming. Did an online study session with them the day before the midterms and explained everything in detail.

Have a class test tomorrow. They've been asking me to do another study session so they can understand it. Try to politely decline but they keep asking.

They expect me to teach them the syllabus. It's like I have an obligation to them. Wtf is this? They don't pay me for college, why can't they just go to the professor?

I hate being an autist, anons. Turns out my "friends" were only friendly so they can get something for it.
>>
I'm a beginning pure mathematics major, just starting real analysis after doing the beginner general classes
I'm kind of interested in philosophy and the question of whether mathematics 'exists' in a real sense as objects, does anyone have any suggestions for reading material on this?
Honestly I can understand mathematical realism better than I can understand the alternate positions which as far as I understand it are nominalism and anti realism but I still struggle a bit
>>
>>14866026
Also specifically looking for material by mathematicians that tries to convince mathematicians that this is an interesting question
>>
>>14866026
I do know there's this couple that has been on Lex Fridman's interview, supposedly they were discussing mathematical abstractions as of they were physical and an actual thing in the universe (wild schizobabel but look into it)
>>
>>14865988
That has nothing to do with you being autistic, it happens to normies too. There are always people who will avoid work by getting other people to do it for them.
>>
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Could someone please explain what's meant by this definition. I don't get it.
>>
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>Second, it is an open question. As long as you can use the fragment shader to generate a noisy pattern, you will get the credit. The noisy pattern should be somehow superimposed over the original color information, i.e., we use the noisy pattern as a perturbation to the original color information.
I have no idea what professor means, but can left be counted as a nosy pattern? I based it off of right's code
>>
How useful would an MS in Logic be for someone trying to do a PhD in theoretical CS later on?
All the CS masters in my city suck ass and don't really focus on TCS but rather on turning you into a code monkey with business perspectives.
But there's this Logic masters that looks pretty good and even has a course on Computability and Complexity.
Of course I could move to another country and do something more directly related with TCS, but I'd like to avoid that.
>>
>>14866746
Study logic yourself retard. You don't need muh Masters in Logic.
>>
>>14866746
at cs departments logic is usually one guy, who kinda wanted to study philosophy but end up studying mathematics. probably going to dress you up as Godel and groom into philosophy.
>>
Is Analysis just Calculus with Topology and proofs? Are there things that are learned in Calculus and not in Analysis?
>>
>>14866909
Calculus' focus is more applied, and you generally won't learn how to derive derivatives of standard functions in a Real Analysis course.
Calculus done rigorously is a subset of Real Analysis. The latter deals with literally analysis of real numbers and algebraic structures on real numbers. The most common structure is of course functions, more specifically smooth "well-behave" functions, which is generally what Calculus is all about. But in Real Analysis, you would deal with weird functions like Thomae, weird sets like Cantor, etc. You would also learn how real numbers, and their arithmetic are constructed. You would learn what it means to raise pi to Euler's number. You would extensively use Topology, more specifically manifolds when doing multivariable Real Analysis. However, Topology is also important in single variable Real Analysis. Stuff like compact sets, and connected sets lead to more general proofs of intermediate value theorem.
Both of them have proofs though. As I said, in Calculus you would learn how to derive derivatives of standard function, which Real Analysis generally wouldn't bother with. Whatever you learn in Calculus that you won't learn in Real Analysis, is purely due to differences in priorities. There is nothing in Calculus that is not in the realm of Real Analysis.
>>
>>14865721
Thank you for taking the time to write this, anon. This was really helpful. Appreciate it.
>>
>>14866319
If the sum of every finite subset is bounded then then sum of the whole set is the supremum of the finite sums
>>
>>14866616
Too regular. "Noisy" generally implies a lack of obvious repetition. Typical approaches to generating noise in a fragment shader involve using fract(f(x,y)) where the range of f is much larger than [0,1] and its derivatives are large so that adjacent fragments produce significantly different values. IOW, |f(x+Δx,y)-f(x,y)|>1, |f(x,y+Δy)-f(x,y)|>1, where Δx and Δy are the amounts by which the texture coordinates differ for adjacent fragments. f should be non-linear.
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>>14867032
So, the sum is only defined for convergent series, right?
>>
>>14867128
Correct.
If the set contains a divergent series then there is no uniform upper bound as required in the definition
>>
>>14865235
I approximated a bunch of fractions so you’re probably more accurate
>>
>>14867140
Great, thanks
>>
>>14858719
Why is Computational Science called Computational Science and not called Applied Computer Science?

Applied Computer Science seems like a more accurate name for the field?

When I read the Landau book he says stuff like:
>Computational scientists solve tomorrow's problems with yesterday's computers; computer scientists seem to do it the other way around

He said that in his lecture videos too.

Does he just dislike the Computer Science field? How is Computational Science not just Applied Computer Science?
>>
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Can anyone recommend me the best textbooks for E&M physics?

What books should I read after Physics II to get to an expert level of knowledge on Electrical Engineering? I feel like my Bachelor's left out way too much
>>
>>14867648
Sorry kid, there's no Kleppner/Kolenkow for E&M. You're gonna have to go straight to Griffits.
>>
what is an easy book to self-study differential geometry?
I tried do carmo's but found it really difficult.
>>
>>14867739
Go back a level and do all the problems. In fact go back to pre algebra and do every single problem in every single math textbook until calculus. Math is a pyramid and if you don't understand something higher level that means there is a knowledge gap in one of the lower levels.
>>
>>14867821
or it's simply a shit textbook. it's not like those don't exist.
>>
>>14867739
>easy
>study
>>
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(a) is 8C2 * 25^6
For (b) i'm getting "26^8 - (25^8 + 8*25^7)" (correct) and "8C2 * 26^6" (incorrect) as my answers. Why is "8C2 * 26^6" incorrect? Since theres 8 possible letters, I restricted 2 of those letters with 8C2 and populate the rest of the letters with 26.
>>
>>14868182
Because you're counting some words several times.
For example the word LLLAAAAA gets counted thrice. Once where the first two L's are fixed and the third random, once where the first and third L is fixed and the second random and a last time where the second and third L are fixed and the first random.
>>
>>14858719
>>14858719
>>14858719
How do you find the canonical partition function for a thermodynamical system? For example 1 of my homework questions is to find it for a system with N identical particles which can have energies E1 = -2/3, E2 = E3 = 1/3 where the particles can exchange places but not move freely or interact.
>>
How long did it take you to reach mathematical maturity? I'm just wondering when I'll not feel like a total brainlet whenever I see real analysis exercises. I've started studying it 1.5 months ago.
>>
>>14868374
The first step to mathematical maturity is humbling yourself, and choosing a book appropriate for your level instead of jumping to muh Real Analysis.
>>
>>14868380
I assumed me being able to eventually solve the exercises means it's appropriate for my level. I struggle, that's all.
>>
>>14868384
If you did not struggle, what would be the point of the exercises?
This is assuming you are not following a retarded book like Stewart.
>>
>>14868489
I don't disagree and see myself improving a ton only due to struggling. I simply wonder if you struggle a lot more in the beginning than in the end.
>>
>>14868499
You keep struggling more because the exercises become harder and longer.
>>
>>14868258
thanks
>>
>>14866819
You need a masters to get into a phd here
>>14866882
>one guy, who kinda wanted to study philosophy but end up studying mathematics
sounds like me
>>
How do you find the discipline and work ethic required to self-study intensely? I can pull miracles when there's a deadline or exam. I struggle to self-study during breaks and get distracted by anime and vidya.
I could study for 8 - 10 hours a day before college (when I was a neet), but now I don't feel like it.
>>
>>14868615
>You need a masters to get into a phd here
So? Do a master's in CS, or math, instead of a highly specific subject like Logic.
>>
>>14868694
Dopamine addiction and lack of exercise.
>>
Why do the days get shorter faster around the equinoxes? The Earth is traveling faster in its orbit around the Sun at perihelion in January. Logically - at least to me as a midwit - it seems that we should be experiencing the biggest shifts in day length in January and the smallest in July.

The day length difference at my latitude:

June 21: +0:03
September 23: −4:48
December 22: −0:08
March 22: +4:52
>>
>>14868694
Things like Bromantane and ALCAR could help upregulate dopamine in a healthy manner. Otherwise, try getting back into it slowly. As in, start by studying for 1 hour a day and slowly increase that day by day.
>>
>>14868781
It's nothing to do with the Earth's velocity. iirc It's simply due to basic trigonometry, something do with the angle between the sun and the Earth's tilt so the rate of change is related to sin or cos (?) and hence is a maximum around the equinoxes when the angle is at a minima.
>>
how do i beat mathphobia
>>
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>>14864203
sorry for wording it badly, i'm mainly wondering how do i represent rules of inference with pure propositional logic (using equivalence rules)

so if for some reason i wasnt allowed to use a rule of inference like hypothetical syllogism, how do i do it with equivalences only?

also how do people do direct proofs, are these the hardest to do? i found i can only solve most problems by doing a contradiction proof because it gives me more things to work with

and can ANY argument be solved with a direct proof, or do some have to be solved by contrapositive or contradiction?

thanks anons
>>
is "for any fixed number $h$" in logic notation $\exists h$ or $\forall h$?
>>
why can't protein structure be calculated/computed with math and chemistry, and must instead by "predicted" by deep learning? Isn't it all just interactions between particles?
>>
>>14869269
second. other anons may correct me, but i don't think "fixed" adds any meaning at all.
>>
>>14869399
Basically true: fixed is used to clarify that the ∀h quantifier is far to the left, so for example ∀h∃x P(h,x) instead of ∃x∀h P(x,h).
>>
can you do this latex thingy on your phone? I'm a phoneposter.
>>
>>14854903
do it both ways and see what happens
>>14843941
no idea, but one of my dreams is to impregnate half of finland and once technology is sufficiently advanced i will go back and impregnate the other half
so just be in finland in 2057 and i'll help you find out
>>14847748
there is an obvious solution
>>14851559
yes high school is literally irrelevant
start asking smarter questions and you'll be fine
>>14851594
i don't know but if your chances of getting in is uncertain you are probably too dumb to pull the lie off anyways
>>14851997
no
>>14853117
a lower bound is provided by 1 day
>>14858450
no
>>14858572
get a new one
>>14862776
how am i supposed to know?
>>14862831
if you meant polynomial, then no
>>14864175
>>14864301
rip in peace nigga
>>14865614
no
>>14869130
with a stick
>>14869429
yes, but if you don't preview and you fuck it up we will laugh at you
>>
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How do I do part b? I don't know how to handle the time period being 4 weeks instead of 1. Do I just multiply the parameter by 4 since the average number of cars every 4 weeks is just the average number of cars per week times 4?
>>
>>14869812
You start by defining random variables.
Let X1 be the number of abandoned in the first week.
Let X2 be the number of abandoned in the second week.
Let X3 be the number of abandoned in the third week.
Let X4 be the number of abandoned in the fourth week.

Those four RV are all i.i.d.
You can use probability generating functions to prove that the sum of independant poisson distributed RVs is poisson distributed too. So in the end you really just have to multiply the parameter by 4.
>>
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Would anyone be willing to explain to me what the limits "c to c+2L" actually means in Fourier series?

I sort of understand that we're supposed to be integrating over a period, right? But why does it still work by adding a constant?
>>
>>14869865
Thanks, anon.
>>
Is there any reason to learn matlab/mathematica (or their FOSS equivalents) instead of py/R/C/C++/fortran if i am learning math purely as a hobby?
My naive opinion is that they seem to be more productive and quicker to learn but slower performance wise and have smaller usage domains than learning a programming language.
>>
>>14869929
You must be drunk or something. c is the start of the period, c+2l is the end of it. Surely this makes sense.
>>
>>14870135
:(
>>
>>14870013
your opinion is more or less right. I recommend julia or python. R is for stats
>>
>>14867648
Landau & Lifshitz, The Classical Theory of Fields.
>>
>>14867648
Smythe. Static and Dynamic Electricity
>>
>>14869269
>>14869399
Far-fetched but might be related: I don't like writing proofs starting with "For all numbers $k$ we have that...". Because then you cannot continue with "Thus we have that..." and use $k$ anymore. I'd rather FIX a number via "Let $k$ be any number.", then do whatever calculation is needed and conclude with something like "Thus for all numbers..." since our fixed $k$ was any arbitrary one.
>>
>>14870013
Since it's a hobby, just go with whatever language you're familiar with and don't waste time learning matlab just because it's got "math" in it. Performance and usage issues are of no concern for you either.
Python is the easiest way in as the other anon pointed out. Julia is a bit more complex but kinda useful. Then you could use C/C++ to optimize something you prototyped in python for example.
>>
>>14870601
What are you talking about shizo?
>>
Any page or book that roughly explains the differences between all these branches of geometry or just fields with geometry in the name? I'm trying to get a better overview of geometry.
>>
The kodaira dimension of a compact complex manifold is 0 right?
>>
>>14869929
If a function is periodic, its integral over one period doesn't depend upon the start and end points. Consider a<b<a+T<b+T:

[eqn]
\int_a^{a+T} f(t) \, dt \\
= \int_a^b f(t) \, dt + \int_b^{a+T} f(t) \, dt \\
= \int_a^b f(t) \, dt + \int_b^{b+T} f(t) \, dt - \int_{a+T}^{b+T} f(t) \, dt \\
= \left [ \int_a^b f(t) \, dt - \int_{a+T}^{b+T} f(t) \, dt \right ] + \int_b^{b+T} f(t) \, dt \\
= \int_b^{b+T} f(t) \, dt
[/eqn]
>>
If I didn't apply for student aid in the fall semester can I still get it for the spring semester
>>
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are set theorists going to hate me if i use such notation for vector entries $x \in \vec{v}$
>>
Why is the axiom of extensionality necessary? Why not define two sets to be equal if they've got the same elements instead?
>>
>>14871415
Yes, it is absolutely tranny behaviour to do so, especially considering all vectors are not tuples.
$\text{Let } \vec{v} = (v_1, v_2, \dots, v_n) \in \mathbb R^n \! , \text{ and let } x \in \mathbb R \text{ such that } ( \exists i \in \mathbb N) (i \leq n \land x = v_i )$
If you use anything else, you are a worthless talentless trash who will never achieve anything.
>>
>>14871587
>all vectors are not tuples
Yes, they are, how do you even define vectors without tuples?
And why not just write $\exists n \in \mathbb{N} : x=v_n$ ?
Also nice of you keeping the rent free.
>>
Find all elements x ∈ D_4 such that (DxHR_270)^23 = V . Show that
you have found all possible solutions.

This is for an intro class on group theory and symmetries but I'm confused how would one go about finding this
>>
>>14871715
To clarify d_4 is dihedral group, h and v are horizontal and vertical flips and r_270 is rotation by 270 degrees
>>
>>14871720
And D is reflection about main diagonal. I know we can simplify inside the bracket to (DxD')^23 where D and D' are the two diagonal reflections but I dont see how that helps
>>
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>>14871587
I'm asking because the notation you're suggesting is tiresome with tensors.
>tranny behaviour
B-but this is a good thing
>>
>>14871715
In a group of order n you have
x^n = 1
for every element. You can prove this with the theorem of Lagrange by considering the subgroup generated by x.
Now D_4 has 8 elements so
x^(23) = x^(-1) * (x^8)^3 = x^(-1)
for every x so it becomes a very simple equation.
>>
>>14871615
>Yes, they are, how do you even define vectors without tuples?
Have you ever read like the first chapter of a Linear Algebra book, you absolute worthless talentless trash?
>And why not just write...
Because there is no $v_{i>n}$ defined, hence not allowed in set theoretic notation.

>>14871799
>I'm asking because the notation you're suggesting is tiresome with tensors.
Define your own notation for 'is an element of vector.' I do it all the time. I have my own notation for the set of upper bounds, linear dependence, continuity, etc.
>B-but this is a good thing
I am not talking about trannies "like" Hunter Schafer. They are not trannies, they are real women.
>>
>>14871415
Yeah because it's incorrect and doesn't make any sense.
The least ambiguous notation I know of is, where $V$ is a vector space over $F$, fixing a basis $\vec{e}_1, \vec{e}_2, \ldots, \vec{e}_n \in V$ and defining the functions functions $P_i : V \to F$ such that $\vec{v} = \sum_{i = 1}^n e_i P_i(\vec{v})$, so $P_i$ acts on a vector to return the i-th coordinate.
>>
>doing some t tests for a doctoral elective
>don't bother with spss because lmao
>shit looks wrong
>way wrong
>pirate spss real quick because something is fucked
>forgot the proper df formula
Nice to know you never stop being retarded.
>>
Is there an intuitive way to understand why lim (x->0) x ln(x) = 0 ?

My intuition always told me that the answer to this limit should be -infinity, since x goes to zero pretty slowly whereas the value of ln(x) decreases incredibly fast between 1 and 0. So it looks like the x term should be negligible, and that the limit should be the same as the one of ln(x). Yet that is absolutely not the case...
For instance the limit (at + infinity) of (e^x) / x is +infinity because e^x increases incredibly fast and 1/x does not decreases to zero that fast. I don't really undertand why this reasoning could not be applied to xln(x).
>>
>>14872340
Consider x=1/u. x log(x) = (1/u) log(1/u) = -log(u)/u.

lim[x->0] x log(x) = lim[u->∞] -log(u)/u

It should be self-evident that the latter tends to zero.
>>
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>>14858719
Physics question here, I'm getting quite pissed off. So basically the question goes:
"You have a coil with N = 10000 windings, a magnetic field B = 1T inside the windings and a current I = 1A running through it. The cross sectional area of the coil is A = 100 * 10^(-4) m^2 and the coil's length is l = 0.4m.

Calculate the induced voltage U, when the voltage is turned off for deltat = 1*10^(-3)s."

Solution is in pic related. I got as far as the formula. But why the fuck does:
$U = -L \dfrac{\Delta I}{\Delta t} =- \dfrac{NBA}{I}\dfrac{\Delta I}{\Delta t} = - NBA \dfrac{1}{\Delta t} = -10 \cdot 10^3 V$
the I disappear here? Why is:
$\dfrac{\Delta I}{I} = 1$
? Or am I missing some shit.
>>
>>14872663
Is it because the rate of change of a constant is simply that constant?:
$\dfrac{\Delta I}{I} = \Delta 1 = 1 [\math] Would it be correct to assume that a differential of a constant, say: d1 = 1? I am also getting confused by the difference between: [math] \dfrac{dI}{dt} [\math] and [math] \dfrac{\Delta I}{\Delta t} . [\math] Can someone clarify. >> >>14872663 Is it because the rate of change of a constant is simply that constant?: [math] \dfrac{\Delta I}{I} = \Delta 1 = 1$
Would it be correct to assume that a differential of a constant, say: d1 = 1?

I am also getting confused by the difference between:
$\dfrac{dI}{dt}$
and
$\dfrac{\Delta I}{\Delta t} .$
Can someone clarify.
>>
>>14872674
>>14872677
>differential of a constant
Man I went full retard here. Hope someone understood what I meant. Simply, is:
Delta 1 = 1 and d1 = 1? I'm so confused lmao.
>>
>>14872663
OR IS BECAUSE THE FUCKING CURRENT IS TURNED OFF FOR 1 ms SO IN THAT TIME FRAME:
$\Delta I = I_{after} - I = 1 A - 0 A = 1A$
? FUCKING HELL MAN.
>>
Physics question for a tourist.

I've heard the Big Bang described as blowing up a beach ball, with the skin of the beach ball representing 4D spacetime. Said beachball is getting bigger so the skin is stretching, making dots on the beachball more distant even though the constants within the beachball are the same (like speed of light).
Using this analogy what represents the air in the beachball? Is that the dark energy/matter that is pushing the accelerating expansion of the universe.
Also, doesn't this imply that there was indeed a singularity, something of a point at the very center of the beachball? Can that point be traveled to in theory, even with infinite dark energy resisting your attempt to "burrow" into it?
>>
>>14858719
I want to calculate the floor space of a pyramid shaped high rise. For a 4 sided pyramid, isn't just the (base * height) /3 * the number of floors?

Also what about a 3-sided pyramid? same but divide by 4? I'm a mathlet please no bully.
>>
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If i am proving a series of statements like
Premise 1
Premise 2
Premise 3
________
Conclusion

and the conclusion is of the form A or B, can i turn this into ~A -> B, and then assume ~A is true, like the hypothesis, and use this to prove C?
>>
>>14872729
prove B sorry
>>
does the possibility of contracting salmonella or how long it lasts depend on the size of the sample eaten?
I ate half a chicken today. I noticed a very small speck of uncooked chicken in the middle, about the size of a ladybug. I ate around it and everything else was fully cooked, but if I had eaten such a tiny piece of uncooked chicken would I still get full blown salmonella or would it just be a one night thing? (or maybe nothing at all?)
>>
>>14872778
>does the possibility of contracting salmonella or how long it lasts depend on the size of the sample eaten?
Yes.
Salmonella is destroyed by normal stomach acid. Eating enough food will raise your stomach pH and increase the chance Salmonella can pass into your small/large intestine where it colonizes.
The infectious dose for Salmonella is >50,000 cells which is about 4 hours of binary division. On an agar plate this is is tiny, about the size of half a donut sprinkle.
If your stomach pH is normal you need a massive dose of salmonella so the sheer numbes will survive the stomach and pass into the intestines.
You're unlikely to get salmonella from uncooked chicken in the middle of cooked chicken unless your salmonella-carrying cook literally took a shit on it
>>
>>14871802
this is very tempting and i spent some time looking ahead in the textbook to understand this solution, but sadly theorem of lagrange is introduced much later in the book, im supposed to somehow prove this with more basic stuff. (namely i dont think i can assume that x^8 = 1)
>>
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>>14872810
thanks mate
>>
will science ever explain the "self-cause" necessary for existence?
>>
>>14871799
An alternate notation for vectors in $\mathbb R^n$ is $x = \vec v \cdot \vec e_i$ for some $i$
>>
>>14872729
What is the start and end proposition, I don't understand.
>>
>>14872722
> Using this analogy what represents the air in the beachball?
That's where the analogy fails. As you said the surface is a 4d spacetime, if you don't have the know-how or the time to work through the math, you will just have to accept there is no "inside".

> Is that the dark energy/matter that is pushing the accelerating expansion of the universe.
Matter has gravity so that actually slows the expansion. The expansion due to the big bang is a constant but Dark Energy appears to be making that expansion accelerate.

> doesn't this imply that there was indeed a singularity
A singularity is an indication of a situation where our current theories of physics no longer apply not that it was actually zero in size and infinitely dense. Instead it would have started out very, very small and very, very dense.
>>
What statistical test should I choose if I want to compare the response (continuous data) of two different groups to one treatment?
MANOVA?
>>
>>14873475
>What statistical test should I choose if I want to compare the response (continuous data) of two different groups to one treatment?
>MANOVA?
I should mention that there is only one level of treatment too which is why I'm not sure if MANOVA is appropriate.
>>
let $(X,\mu)$ and $(Y,\nu)$ be measure spaces and consider the space $(X \times Y, \mu \times \nu)$ with the product sigma algebra. call a product set $A \times B$ "boring" if $\mu(A)=0$ or $\nu(B)=0$.

is every measure zero subset of $X \times Y$ a countable union of boring product sets?
>>
>>14873654
No. Consider the line segment $L=\{(x,x)\in\mathbb R^2\mid x\in[0,1]\}$ with the ordinary Lebesgue measure.
Clearly, any subset of L has the same measure when projected to either coordinate, so the boring subsets of L are sets of the form Z*Z, for some zero-measure Z in [0,1].
Now, suppose L is a union of such Z_i*Z_i, then [0,1] must be the union of Z_i.
Since [0,1] has non-zero measure in R, it is not a union of zero-measure sets, so L is not a union of boring sets.
>>
Maybe I'm dumb but why are the energy levels of a quantum dot always depicted as evenly spaced? If it's indeed a particle in a box system they should go like $n^2$.
>>
>>14872729
Yes you can, if you can prove ~A -> B (or alternatively ~B -> A) then you can use the rule of replacement to turn it into A v B
>>
>>14873692
ah, I see. thanks, anon
>>
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>>14858719
Good morning /sci/entists!

A couple days ago I was making a thread about measuring if random numbers can be psychically tampered with (research strongly implies no). It got jannied for some reason while I was working on the code and janny gave me a 24 hour banny.

I am going to repost some things from it here so the math will render again because I can see math on warosu.

>>
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>>14873833
(Math repost 1)
>reposting for math
So if i understand correctly, you're taking two random digits and concatenating them, and i assume every digit has an equal chance to be selected. DESU i don't understand what SQUASH means and i'm also not a programmer, i'm only asking to make sure your numbers are uniformily distributed (i.e. every number has equal chance of being selected), it seems that your method is fine. Again i'm not a programmer i'm just going to give you the math you need with some rudimentary explanations.
In this case your expected average will be 99/2 = 49.5, that is if you generate $n$ random numbers according to your above rule and take their average then you should expect a number around 49.5 (but it's not likely you will get 49.5 exactly!)

Also i want to say before i explain the math that you can never "prove" a statistical result is anomalous, you can only say something like
>"there's a 0.00000000001% chance i could've gotten this result according to my assumptions, so either an extremely rare event happened or my assumptions are incorrect, and since an event like that is extremely rare it's more likely my assumption is incorrect"
So i think you understand where we're going with this.
So let's say you generated $n$ random numbers (again according to the above rule) and found their average to be 56.1 after you do some psychic meddling thingy where you try to increase the average, so does this provide evidence for psychic meddling? what is the probability of getting 56.1 or a larger average if psychic meddling wasn't real? we can actually calculate this probability, it's actually equal to [eqn] \frac{1}{\sqrt{2\pi}} \int_{Z}^{\infty} e^{-t^2/2} \; dt[/eqn]
>>
>>14873836
(Math repost 2)
>reposting for math
Where $Z$ is called the $Z$-value and is calculated as follows [eqn] Z = \frac{\mu - \mu_0}{\sigma / \sqrt{n}} [/eqn]Where $\mu$ is the average you got (in this case 56.1), $\mu_0$ is the hypothesized or expected average (in this case 49.5), $n$ is the number of random numbers you generated and $\sigma$ is the standard deviation of your sampling distribution. For a discrete uniform distribution the standard deviation will be [eqn] \sigma = \sqrt{ \frac{m^2-1}{12} } [/eqn]Where $m$ is the number of elements of the set from which you're choosing random numbers, for the case of generating numbers between 0 and 99 then $m$ will be 100, if you're generating numbers between 0 and 999 then $m$ will be 1000, etc.

So i'm going to put all what i just above together to give you an example how you calculate such a probability in practice, first assume we have generated a 1000 numbers between 0 and 99, now start by calculating the standard deviation, then use it to calculate the $Z$-value
[eqn] \sigma = \sqrt{ \frac{100^2-1}{12} } \approx 28.866 [/eqn]
[eqn] Z = \frac{56.1 - 49.5}{28.866 / \sqrt{1000}} \approx 7.230 [/eqn]
So now we can use this to calculate the value of the integral
[eqn] \frac{1}{\sqrt{2\pi}} \int_{7.230}^{\infty} e^{-t^2/2} \; dt \approx 2.414 \cdot 10^{-13} [/eqn]
This probability is EXTREMELY LOW! therefore it provides strong evidence that psychic meddling is real, and in fact such a value would be more anamolous if our $n$ was larger.

It's very difficult to explain where the math above comes, if you want to understand where these formulas come from then you need to study statistics. For a youtube channel on statistics i only know https://www.youtube.com/user/jbstatistics/videos

(2/2)
>>
What's a good paper/book to start understanding male sexuality/sexual behaviors?
>>
>>14873853
I don't know, but avoid Sex at Dawn.

The central argument of Sex at Dawn is basically "The author wants to see his wife star in a 50 man gangbang, therefore all men want to see their wives star in a 50 man gangbang."

He then writes a bunch of pseud nonsense about "sperm competition" to pretend his fetish is some fundamental piece of human sexuality instead of just a weird thing he himself is into.

>tl;dr: Man tries to use science to project his weird fetish onto human behavior.
>>
Let G be the set of 2×2 real matrices A with both eigenvalues having absolute value equal to 1.
Is G a group with respect to matrix multiplication?
>>
>>14873927
Yes.
>>
>>14873959
why?
>>
>>14873968
Multiplication of matrices is assotiative.
The identity matrix has only the eigenvalue of 1.
If no eigenvalue is 0 then a matrix is invertible.
If $A$ has the eigenvalues $\lambda_1$ and $\lambda_2$ then $A^{-1}$ has the eigenvalues $\bar \lambda_1$ and $\bar \lambda_2$ which will both have absolute value of 1 too.

What more do you need?
>>
>>14873927
Ignore my other posts. It's not actually a group.
[eqn] \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix} = \begin{pmatrix} 0 & 1 \\ 1 & 1 \end{pmatrix} [/eqn]
The matrices on the left have eigenvalues with absolute value of 1 but the matrix on the right has the eigenvalues
$\phi = \frac{1 + \sqrt{5}}{2}$ and $- \frac{1}{\phi} = \frac{1 - \sqrt{5}}{2}$ which have different absolute values.
>>
>>14874056
ah very nice counterexample, wouldnt have found it. thanks
>>
>>14874056
Arguably, [[1,1],[0,1]] doesn't have two eigenvalues, as it isn't diagonalizable. I haven't been able to find any counterexamples with diagonalizable matrices, so G might be closed under this more strict definition.
>>
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Can you simplify this further?
>>
>>14874272
Consider:
[eqn]
A = \begin{pmatrix}0 & -1 \\ -1 & 0\end{pmatrix},\,B = \begin{pmatrix}1 & -4 \\ 0 & -1\end{pmatrix}, AB = \begin{pmatrix}0 & 1 \\ -1 & 4\end{pmatrix}
[/eqn]
A and B both have eigenvalues of ±1. AB has eigenvalues of 2±√3.
>>
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Can someone explain to me what happens here?
>>
>>14874505
Use partial fraction decomposition.
>>
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>>14858719
my hp-50g broke a long time ago. I don't really need a calculator too much anymore since I graduated but man I really miss it. Any risk of buying one on ebay? is there a repair service out there for these things?

I fucking love reverse polish notation, it's so good. I don't really jive with the lcd screen calculator meme it's like at that point let me just use my phone
>>
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how can I induce early greying
>>
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>>14858719
What is theta doing here? What does this mean?
I thought theta was an angle.
Could I please get a run down of theta's uses?
>>
Retard here, can someone explain how I can do this?

A U B = {a,b,c}
>>
>>14874550
theta is a letter and can be used a symbol for whatever
your pic looks like theta is just being used to represent vertical displacement
>>
>>14871615
>how do you even define vectors without tuples?
A vector is simply an element of a vector space. Not all vector spaces can have their elements written as tuples.
>>
frens, I'm struggling with this one. Why can't I into venn diagram word question? THis question is worth 7 marks
>>
>>14874565
5 want to take French and Latin, and 3 of these want to take Spanish too. So that means 3 people want to take everything, and 2 want to take just French and Latin.
From here, you can subtract the total numbers that want to take each language from the values that were explicitly given to you
>>
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why is the force on wire AD attractive?
>>
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>>14874595
>>
>>14874604
thanks for the thumbs up
>>
>>14874589
Thanks you, anon.
>>
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can this be solved for T?
>>
>>14874505
Partial fraction decomposition, then

1/2k - 1/(k+1) + 1/2(k+2)
= 1/2k - 1/2(k+1) - 1/2(k+1) + 1/2(k+2)
= (1/2k - 1/2(k+1)) - (1/2(k+1) - 1/2(k+2))

So the sum is a telescoping series.
>>
>>14874556
The cardinality of a (finite) power set is 2^n, where n is the cardinality of the set you're taking the power set of. So in this case it'd be 2^3, or 8. Or you could just write out all the sets and count them. Don't forget the empty set.
>>
>>14874750
Shut the fuck up worthless talentless trannies
>>
Trying to fix my brain by learning math.
I wanna start from the very beginning and I wanted to know how I should move on after mastering a subject?

I was thinking of like how they did it in my school system.

Basic Arithmetics>Algebra>Geometry>Trigonometry>Calculus>Statistics

Would that be fine?
>>
>>14874822
Also, how do I work on my number sense? Should I just print out worksheets and drills?
>>
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need help, pls, i beg you
>>
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When I look at the definition of anything in math it just looks like numbers and Greek symbols threw up.
What are the people who write mathematical definitions smoking?

Serious question, I want an answer... How do you read this and what is the point of this? What are they trying to say?

"Where 0 is the zero vector in A"
What?
>>
>>14874931

Where do you begin to get a grasp on why they talk like this and what point they are trying to make? Should I start with these kinds of 'definitions' for 3rd grade math? Does such a thing exist?
>>
>a) minimize F(x) where F is deterministic
>b) minimize E[F(x)] where F is stochastic
Is there a theorem that can help me compare min of a) and min of b) (i.e. which is larger)? I don't think Jensen's inequality helps me because the argmin of b) is not necessarily E[argmin of a)]. I hope my question isn't too vague.
>>
>>14874931
>"Where 0 is the zero vector in A"
>What?
because different vector spaces can have different forms of 'zero' element in them. For instance
[eqn]\begin{bmatrix}
0 & 0 \\
0 & 0\\
\end{bmatrix}
,
(0,0,0)
,
0x^2+0x+0
,
0[/eqn], etc.
are different forms of zero vector on their respective vector space, so you have to specify such element belong to that sort of set with rules attached to it.
And it's not like they pulled the definitions from under the sleeves, they came as a result of being playing around with similar stuff for a while, and finally converged and condensed in a simple and short (ok this is arguable) definition that include the studied cases
>>
>>14874541
> fucking love reverse polish notation, it's so good. I don't really jive with the lcd screen calculator meme it's like at that point let me just use my phone
There's an emulator app called 48sx that fully replicates the 48g series. The only problem is you need a specific phone that has an IR blaster to make full use of it, and most phones since 2015 don't have one.
>>
>>14874313
you could factorize the numerator using the binomial formula, but it wouldn't add much, frankly
>>
>>14873173
>As you said the surface is a 4d spacetime, if you don't have the know-how or the time to work through the math, you will just have to accept there is no "inside".
What's a better analogy then? Can you like me to some graphs or a video that visualizes this? I can't wrap my head around the singularity because my understanding of physics as a casual is limited by the world around me. If the singularity inflates then expands, it's expanding into "something" that forms the boundary between the universe and the not-universe. So even if within the universe itself you cannot locate a point where the big bang began, if the universe is expanding equally in all directions the reverse vectors will point at some kind of center, even if that center cannot be practically traveled to since space is moving away from it.
>>
If silver has 47 protons why does it have a weight of 107 amu? Aren't neutrons and protons supposed to be matched, or close to matched?
>>
>>14875043
and how many neutrons does it have?
>>
>>14875043
I think as the atomic number gets higher, the number of neutrons tends to outpace the number of protons.
You also get more isotopes of a single element
>>
>Show that if α and β are nth and mth roots of unity, respectively, then the product αβ is a kth root of unity for some integer k.

I think I need some argument for why a^nm and b^nm are roots of unity, then I get (ab)^(nm) and nm = k, but I'm not sure what that argument is. Could someone point me in the right direction?
>>
>>14875102
Nevermind it's extremely obvious & I'm dumb
>>
Where the fuck are they getting these numbers from in the inequality?? I understand what they're expressing and I understand why it works. I just don't understand how they're picking out those terms they're using? Is there any rhyme or reason to this at all?
>>
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Can someone please explain in English and with numbers what an 'Affine Set' is?
What is this trying to say?
>"If the line through any two distinct points in C lies in C"
Why wouldn't a line though the C points lie in C?

>"We have theta x1 +(1-theta)x2"
Why do we have this?

>"C ontains the linear combination of any two points in C, provided the coefficients in the linear combination sum to one."
Why? Are we summing to one here? Why not -19 or tree fiddy?
>>
>>14875124
I'm shit at math but I'm fairly sure T(n-1) is supposed to be another way of expressing 0, since your condition was that n=1 is the maximum.
So n < c (n-1)^2 is again expressing that n is bounded by the region up to n=1
>>
>>14875076
125 apparently, but idk why

>>14875083
Surely there's a pattern or mechanic?
>>
>>14858719
If space has been expanding, then in addition to the Doppler effect, light from a distant galaxy should also get stretched out by space expanding along its path. We would expect this stretching too occur more for light that travels a longer path, therefore older light from more distant galaxies will appear redder. Have cosmologists already taken this into account when concluding that dark energy is a thing? Is there like a math equation for it or something?
>>
>>14875037
> Can you like me to some graphs or a video that visualizes this?
Sabine is always a good place to start.

https://youtu.be/l3C_db2RjKo?t=4
>>
>>14875221
https://en.wikipedia.org/wiki/Hubble%27s_law
>>
How far away would I have to be from a pressure washer, with an out-the-nozzle pressure of 1200 PSI, for it to be as harmless as a walmart squirt gun?
>>
>>14875153
predicting properties of nucleons is incredibly hard as it involves QCD calculations, which we can only do with any reasonable accuracy for very light nuclei.
the nuclear shell model and the liquid drop model are two quasi-successful models of the atomic nucleus, but there's no perfect way to predict the most stable number of neutrons for an atom with Z>~20
>>
>>14875221
>>14875408
There's also

https://en.wikipedia.org/wiki/Friedmann_equations
>>
>>14875401
So the univerise is a sheet of paper being stretched in all directions, and for an ant on that sheet you cannot find the location of the the initial singulrity because it's te entire manifold, stretched out. Trying to find the reach the center is like trying to reach the engine of a train going in the same direction you are facing, while standing on a train going in the opposite direction. The singulrity is everywhere at once.
So this "embedding space", or 5th dimension, if it exists, would hypothentically have a point on it associated with the beginning of the universe at a coordinate, but describing such a thing would be beyond physics because physics by definition can only describe the universe, from within the universe.
Am I getting this right?
>>
>>14875478
You are making the common mistake of confusing the word universe with the observable universe. Whenever a scientist says universe 99 times out of 100 they are talking about the observable universe. What happens outside of our little patch of space-time we will never know because of the speed of light limitation. So we do not even know if the 'universe' is finite or infinite. Get this idea of a singularity out of your head. The big bang theory doesn't say there was one. All we can say is that the volume of space-time we can observe was smaller in the past and then it began to expand.
>>
>>14860284
> upside down triangle
... which way up is a triangle?
>>
>tl;dr what motivates the notion of "spectrum" in operator theory?

Let $T$ be a bounded operator on some Hilbert space. I get why one would want to study its eigenvalues: if $\lambda - T$ is not injective, this is *obviously* useful, as one can describe the restriction of $T$ to the eigenspace in a very simple manner. What's *not obvious* to me is what makes the non-point spectrum interesting. Why should I care about the scalars $\lambda$ for which $\lambda - T$ is not surjective?

"Because the spectral theorem for normal operators is useful" feels like too much of an ad-hoc answer. Suppose we didn't know there is such a theorem - how would you motivate the study of spectra?
>>
Does anyone know of any Real Analysis book that covers Telescoping series?
>>
>>14875414
Same anon, but is there an equation that tells me how far a stream of water would have to go, given a starting pressure, before it drops down to a lower pressure?
It starts at 3000 PSI/2 Gallons per Minute/243 MPH, which i got off of google, and should end at 40 PSI, aka how much a super soaker is rated for. It just leaves the nozzle with that pressure, and goes in a straight line to make things simpler until it reaches the target pressure, and ya measure the distance it went.
>>
>>14874750
Ah, thanks, anon.
>>14874753
Don't miss your meds?
>>
>>14874505
Good you have found your place in /sqt/. Don't bring your shitty homework questions in /mg/ again FAGGOT
>>
>>14858719
could someone explain to me in retarded terms what a Torsion Free Group is? I just cant wrap my head around it, tenkiu
>>
>>14875715
what part of the definition do you not understand? torsion free means every non-identity element has infinite order. the simplest example is Z (take any non-zero integer and add it to itself any finite number of times - this will never give you 0, hence every non-identity element has infinite order).
>>
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>>14875128
>Why wouldn't a line though the C points lie in C?
see picture

>>"We have theta x1 +(1-theta)x2"
>Why do we have this?
that is the formula for a line through two points

>>"C ontains the linear combination of any two points in C, provided the coefficients in the linear combination sum to one."
>Why? Are we summing to one here? Why not -19 or tree fiddy?
if a point is on the line then it is a linear combination as shown in your picture
and theta + (1 - theta) = 1
although this is not a necessary condition
>>
Let $X,Y$ be two sets, and let $f: X \to Y$ and $g: Y \to X$ be injections.
Prove that there exists subsets $A,B \subset X$ and $A',B' \subset Y$ such that
$B = X \setminus A$,
$B' = Y \setminus A'$,
$f(A) = A'$
$g(B') = B$.

How do you prove this without using advanced theorems like Knaster-Tarski?
It ultimatively involves finding a set $A \subset X$ with $A = X \setminus g(Y \setminus f(A))$.
>>
If a triplet of homogeneous linear equations has rank 2, will it still have infinitely many solutions? Or does it need to be rank 1. Geometrically, I can see that it needs to be rank 1, i.e., all the three lines must be coincident, i.e., every equation can be expressed as a multiple of exactly one other equation. But wikipedia says all it needs is for the matrix to be singular, but that includes rank 2 equations.
>>
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Programmer here, starting uni soon. I want to know how to find knowledge gaps in math. I've got a bit of calculus but it always feels isolated. My mental model is that one topic builds another, maybe it's wrong?
>>
>>14875758
Any system of homogenous equations has infinitely many solutions. For any solution which satisfies all equations, multiplying all variables by the same scalar will produce a solution which satisfies all equations.
>>
>>14875758
Equations in 3d space are visualised as parallelograms not lines.

>>14875923
>Any system of homogenous equations has infinitely many solutions
Wrong. $x + y = 0; 2x + y = 0$
>>
>>14875923
no
>>14875758
if you have 3 equations that has rank 2 you will have one "free" dimension
you will still have infinite solutions along a line, the line will just not be parallel to the first two equations
if all three equations are a multiple of exactly one then you would have 2 free dimensions and your possible solutions will be an entire plane
in either case you will have infinite solutions
>>
>>14875844
if you want a general top-down view of math then watch Introduction to Higher Mathematics by Bill Shillito
>>
$8\, |\, b \wedge 10 \, |\, b \implies LCD(8, 10)\, |\, b \implies 40\, |\, b$

could you substitute the $\implies$ with $\iff$. If not, why doesn't this work?
>>
>>14875417
Huh. can I rely on elements having a matched number of protons/electrons?
>>
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bros, do you think this is enough. Or will I have to go into more detail?
>>
>>14876126
Yes that is always true.
>>
>>14875950
>>14875955
Thanks.
>>
If tactical nuclear weapons are used in Ukraine, would the EMP affect the electronics in Europe?

t. increasingly nervous Europoor contemplating getting a bicycle or a vintage moped in case my car is disabled.
>>
Guys, how should I go about solving this?
$f(x)\frac{1}{x(x+1)}$
Calculate f(1) + f(2) + ... f(100)
>>
>>14876624
You'd have to be pretty damn close to be affected badly. It's still the inverse square law at work. So if you can't see it you'll be fine.
>>
>>14876913
[eqn]\frac{1}{x(x+1)} = \frac{1}{x} - \frac{1}{x+1}[/eqn]
When you sum these terms:
[eqn]\sum_{x=1}^{100} \left(\frac{1}{x} - \frac{1}{x+1}\right) = 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \dots[/eqn]
You end up with a telescoping sum, i.e. a sum where two successive terms cancel each other out, leaving only the first and the final one. Therefore:
[eqn]f(1) + f(2) + \dots + f(100) = 1 - \frac{1}{101}[/eqn]
>>
>>14876944
>telescoping sum
Holy shit, that's a new one for me, on this collection I'm reading sums and progressions are presented on the second book, I think that's the author's way of priming us for it. Thank you a lot, anon, I'm going to dive in on this kind of sum and answer this question. One more thing, how did you deduce this? I don't have this kind of intuition lol
$\frac{1}{x(x+1)} = \frac{1}{x} - \frac{1}{x+1}$
>>
>>14876913
0.9899999999999997
>>
>>14876913
Let me stream of consciousness this for you
Looks like I'd get some nice fractions. Why not try out a few values?

1/2 + 1/6 + 1/12

oh it's getting harder to calculate what shortcut can I reach for? ah, it's just twice the sum of all integers 1 through x, I know that sequence

+ 1/20 + 1/30 + 1/42

ok this isn't giving me any numeric pattern I know what to do with, what about the formula... I mean if the bottom term is itself the sequence of consecutive integers, I should be able to split it this shit into something simpler, right? Oh, the fraction, the denominator is a product, after all.

1/x + 1/(x+1) = (x + 1 + x)/(x*(x+1))

ok, looks like I can do the usual trick with negatives to cancel out

-1/(x+1) + 1/x = (-x + 1 + x)/(x * (x+1)

fucking got it
OK, so now this should be much simpler, I guess I can see it must be positive because the positive term can always be paired with a negative one with a bigger denominator.. oh wait that's retarded, there were no negatives to begin with in the original equation.. but wait, this is the answer. If you pair up the terms according to the original term they got split from, the first term in the next pair cancels the second term in the previous. So if we re-bracket the pairs starting by skipping the very first linear term, we end up just having the first and last term remaining in the sum.

That means it's 1/1 - 1/101. Fuck, this would look nicer with Latex but I already feel like a cuck writing out my thought process. Well, let's check this for a small sum in case I fucked something up and end up looking like a retard.

1/2 + 1/6 + 1/12 + 1/20 = (20 + 12)/240 + 8/12 = 2/15 + 2/3 = 12/15 = 4/5... fuck, that took way longer to calculate than I thought. Am I losing it? Wtf is wrong with me?

Anyway, 1 - 1/5 = 4/5 so that checks out. Ah, wait... if I just made a table of the first few sums instead of just terms, this pattern would have been immediately obvious. But I guess this way I have a general formula...
>>
>>14876989
Not >>14876944 btw. just a random retard who started replying without refreshing and incidentally answered >>14876971
>>
>>14858719
where are all the places that the "water pipe" analogy for electricity break down
no, i don't want to hear about fields
just in wires, imagining current and volts and stuff - where does the pipe analogy break down, like with Bernoulli's principle?
does elec in wire have a BP style analog that passes?
>>
>>14876999
Thank you too, based triples, it's always good see different approaches to a question, I'm noting down both of the anwers.
>>
>>14876986
Try your loop from 100 going down to 1.
>>
>>14877052
0.4900990099009901
>>
>>14876126
yes or else they would be ions and have a net charge
>>
Please give a short example of a vector space that isn't in Rn. Something that is easily memorizable.
>>
Let $f$ be a polynomial of degree 3. If there exists polynomials $g, h$ of degree $\ge 1$ such that
$f = gh$, prove that $f$ has a root.

I'm already aware that I should have wrote out $f$ as $f(x) = a_0 + a_1x + a_2x^2 + a_3x^3$,but past this point I'm stuck.
Any ideas for next steps?
>>
will aaron judge hit his 61st home run tonight?
>>
>>14878363
the cards say no
>>
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How does Associative and Commutative Laws work when things are nested, in formal propositional logic?

Eg if i have: ((A v B) v C) v D

and i want: (A v D) to be together.

do i have to do:
((A v B) v C) v D Start
((B v A) v C) v D Com
(B v (A v C) v D Ass
(B v (C v A) v D Com
((B v C) v A) v D Ass
(B v C) v (A v D) Ass

Is the last Ass legal? I feel like i am breaking rules but dont know how else to get A out of the braces.
>>
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How did this Bayes Rule equation get to the p(y|theta= ... bit at the bottom?
I don't understand how the p(z|y,theta) at the top logically leads to the part at the bottom.
>>
what does it actually mean to divide by a negative number? an apple split in half is simple to understand since it's very common in real life, but what is the opposite of that, splitting by negative half? like how are you supposed to visualize that, does the apple just disappear into a negative dimension where it is split in half there or what
>>
>>14878702
You are not supposed to visualise anything. This is math not art, fuck off. Division by negative number is multiplying by the multiplicative inverse of an additive inverse. If you think anything else you are worthless talentless trash.
>>
>>14878612
Yeah thats fine. If you add an extra set of parenthesis, perhaps it's easier to see that it's an instance of the standard associative rule:
(((B v C) v A) v D)
((B v C) v (A v D))
>>
>>14878721
you can clearly visualize other operations with negative numbers, why you aren't allowed to do the same with division? so answer me, what happens to the apple as you divide it by a negative amount of times?
>>
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>>14878333
I assume you're working over the rationals and not the complex numbers? If f=gh is a polynomial of degree 3 and g,h are polynomials of degree greater than or equal to 1, then exactly one of the is degree 2 polynomial and one of them is a degree 1 polynomial. Now you need to state why one of those polynomials has a rational root and explain why that implies that f has a rational root.
>>
>>14876107
It works if you switch it to least common multiple (LCM) instead of least common denominator, which doesn't apply here since we're not dealing with fractions.
>>
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>>14878740
Tyvm anon
>>
>But then, by definition, $z = p \pm^h r/s$
Someone explain this to me. What does the $h$ in the exponent of the plus or minus sign even mean? Also he never defined $z$ at all. I assume that starting from (3.2.6.4) he added $v_p \left(\frac{1}{y} \right)$ to the inequality to get
[eqn]v_p \left(\frac{x}{y} - 1 \right) \geq min \left(v_p \left(\frac{x}{y} \right) , \underbrace{v_p \left( 1 \right)}_{=0} \right)
[/eqn]
and then defined $z = \frac{x}{y}$ but he never explicitly said so who knows?
>>
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Forgot pic
>>
>>14878628
It's simple cross multiplication.
>>
NEW

>>14879691
>>14879691
>>
does anyone have a video lecture on this topic?
https://openstax.org/books/university-physics-volume-1/pages/14-introduction
Chapter 14: Fluid Mechanics
i tried reading the textbook but i dont get it
can someone link me like a video lecture or something

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