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Formerly >>15104536

>what is /sqt/ for?
Questions regarding maths and science. Also homework.
>where do I go for advice?
>>>/sci/scg or >>>/adv/
>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?
scholar.google.com
>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?
images.google.com
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?
sites.google.com/site/scienceandmathguide
4chan-science.fandom.com/wiki//sci/_Wiki
math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>online courses and lectures?
khanacademy.org
>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
>ask anonymously
>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 reading your handwriting
>I'm not flipping that sideways picture
>I'm not google translating your spanish
>don't ask to ask
>don't ask for a hint if you want a solution
>xyproblem.info
>>
Unanswered questions:

Maths questions:
>>15106189 [Partially answered in >>15106318]
>>15106588
>>15110908
>>15115574
>>15116344 [Basically no one bothered going through with writing the proof that the second series doesn't converge because it "takes too long to switch signs."]
>>15116499
>>15117798 [Yes.]
>>15119114
>>15128426

Physics questions:
>>15115655
>>15120257
>>15123324

Chemistry questions:
>>15106334
>>15127104

Biology questions:
>>15110445
>>15121151

Engineering questions:
>>15121662 [IIRC yes.]
>>15122047

/g/ questions:
>>15108375
>>15113929
>>15116240
>>15116469

Maid questions:
>>15124859

Stupid questions:
>>15105955
>>15106120
>>15108092
>>15108183
>>15113346
>>15114619
>>15114728
>>15115189
>>15116378
>>15119072
>>15123008
>>15123277
>>15125661
>>15126723
>>
U := {f | f is not continuous at x = 0.5}

this is a subset of the set V of all maps from [0, 1] to R. I have to show that this isn‘t a vector subspace of V. The addition and scalar multiplication on V is each declared pointwise.

Can I say the 0-element (f: [0, 1] -> R with f: x -> 0) is obviously continuous at x = 0.5 and therefore not in U. And since U doesn‘t have the 0, it can’t be a vector subspace. Can I do it like this?
>>
>>15128769
Sure, that's correct.
>>
>>15128794
Great
>>
I'm self teaching electromagnetism and working on Gauss' law at the moment. I'm having hard time with this simple problem:
> Two large metal plates of area 1.0 m2 face each other, 5.0 cm apart, with equal charge magnitudes |q| but opposite signs. The field magnitude E between them (neglect fringing) is 55 N/C. Find |q|.

The answer from the solution manual is:
> The surface charge density is given by [math]E = \frac{\sigma}{\epsilon_0} \implies \sigma = \epsilon_0 E = (8.85e-12)(55) = 4.9e-10 C/m2 [/math]
> Since the area of the plates is [math]A=1 m^2[/math], the magnitude of the charge on the plate is [math]Q = \sigmaA = 4.9e-10 C[/math].

I don't get it, as here is my reasoning:
At any point between the plate, the electric field from each plate should apply leading to, du to the superposition principle: [math] E_{net} = 55 N/C = E_{plate_1} + E_{plate_2} = 2E_{p}[/math], as the plates are same charge but opposite sign, so their field are in the same direction between them.

We would thus have [math]E_{p} = \frac{\sigma}/{\epsilon_0} [/math] and then [math]E = 2 \frac{\sigma}/{\epsilon_0} [/math].
Knowing that [math]\sigma[/math] is the surface charge density on one plate [math]sigma = \frac{|q|}{A} = |q|[/math], so finally:
[math]|q| = \frac{E \epsilon_0}{2} = \frac{(8.85e-12)(55)}{2} = 2.4e-10 C[/math]


So guys, where is the brainfart in my reasoning?
>>
>>15128744
the base baths i've seen usually involve heavy duty gloves and tongs, no need for full hazmat but yeah apparently that shit's nasty
>>
Assuming [math]a_n > 0, b_n > 0, \lim b_n \to \infty[/math], then [\lim \frac{a_n}{b_n} = \infty \implies \lim a_n - b_n = infty[/math]
Proof.
[eqn]\forall _{M > 0} \exists _{n_0 \in \mathbb{N}} \forall _{n > n_0} b_n > M \land \frac{a_n}{b_n} > M \iff a_n > M b_n \iff a_n - b_n > b_n(M-1) > M[/eqn]
Is it possible to generalize this result further? I was specifically trying to prove that [math] \lim \frac{a_n}{b_n} = \infty \iff \lim a_n - b_n[/math] but I couldn't find anything.
>>
>>15128812
Problem lies in your interpretation of solution that was given, field E in solution is already combined field of both plates.
To see this calculate what is field given by one plate, Spoiler alert it is E=sigma/(2 epsilon). You are missing 1/2 in your expressions for Eplate.

If you are not certain how to obtain 1/2, when you apply Gauss law to the surface you envelop some area of plate with rectangle, but one side of the rectangle does not lie on the plate. Both sides are sticking out, one on the front and one at the back. for both sides you have EdS which combine. Even thou fields from front and the back are oriented differenty you also have that normal vectors of surfaces are in oposite directions aswell. This produces factor of 2.
>>
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I'm doing some HPLC ( not a chemist/biochemist at all ) and was wondering why Primary Metabolites tend to be polar compounds whereas Secondary Metabolites tend to be non polar.

Came up whilst reading about column selections.
>>
>>15128947
Everything is positive.
If [math]b_n[/math] is bounded above, [math]\displaystyle \lim_{n \to \infty} a_n - b_n = \infty[/math] implies [math]\displaystyle \lim_{n \to \infty} \dfrac{a_n}{b_n} = \infty[/math].
If [math]b_n[/math] is bounded below, [math]\displaystyle \lim_{n \to \infty} \dfrac{a_n}{b_n} = \infty[/math] implies [math]\displaystyle \lim_{n \to \infty} a_n - b_n = \infty[/math]
>>
>>15128956
>Secondary metabolism (also called specialized metabolism) is a term for small molecules that are involved in ecological interactions, but are not absolutely required for survival
Primary metabolism = oxidize the fuck out of it so it's water soluble and can be pissed out
Secondary metabolism = make toxins that will linger in fatty tissues forever
>>
I define the function f: {0} in x -> 0 in R. So it's a function, the domain of which has only one value. Is this function continuous?
>>
>>15128726
What is analytical chemistry like as a class? Can anyone give me a QRD? Chemistry was one of my favorite classes and I just realized I can take analytical chem as an elective for my major, but I haven’t thought about anything too chem related for 2.5 years. What should I know to be prepared for a class like analytical chem?
>>
>>15129090
Yes.
>>
>>15129095
bunch of autism about identifying and propagating error, differences between glassware, titrations, bit of kinetics and thermodynamics (finding activation energies and rate constants and such)
It's a brutal grind, but the good kind that builds character if you have the mind for it
>>
>>15128726
Say nitrogen has a molar mass of approx 14 g/mol and a density of 1.17 kg/mol. How do I calculate the volume of 1 mol of nitrogen?

I tried and get: 1.99 * 10^26 m^3, did I do correct or wrong anons?
>>
>>15129217
Or did I fuckup? Is 1.02 * 10^(-5) m^3 correct?
>>
>>15129217
Molar volume is molar mass divided by density
>>
>>15129246
Thanks anon, what I have is correct. It explicitly states to note to volume for 1 mol of gold, so I think that's:
>molar volume * 1 mol.
I punched that into Google and got the correct value.
>>
have to take into to fluid mechanics soon. anyone remember what differential equations you need for the class?
>>
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is this correct? n is a natural number
>>
>>15129277
Navier Stokes/Advection/Euler equation and continuity equation
>>
>>15129299
thank you
>>
>>15115655
probably not. the effect is also known as the "intermediate axis theorem", because it only occurs when an object is spinning about its second principle moment of inertia, and its pretty easy to see that throwing a knife would be spinning it around its third principle moment.
>>15116469
probably. its easy in one direction but hard in the other. i think thats the only requirement.
>>15105955
i like cute things.
>>15119072
its likely that you dont hear or feel things in dreams, or really even experience dreams at all. there was a phenomenon that occurred after television was first invented: previously in history, people had reported dreams being in color, but after television was widespread (and of course it was in black and white at first), people reported dreaming in grayscale. and then after color TV became the norm, people started reported dreaming in color again. this phenomenon is often cited as evidence that people dont experience dreams, they only remember them, and you brain fills in the details later as if they occurred in the past, but in reality your brain is creating them in real time. personally, anecdotally, ive had dreams where it feels like something (a person, a place, etc) is extremely familiar to me, as if ive known them my entire life, but in actuality are entirely novel. so personally im pretty susceptible to the idea that dreams fuck with your sense of time hardcore.
>>
[math]\lim_{n \to \infty} \sin(nx)[/math]

I found a limes for this expression, but it's not a function. I evaluated that the limes has to be a line from -1 to 1 at all x = pi * (1 + 4k)/2n with k being in Z and n in N. Obviously this is not a function, but interestingly these lines are countably finite and the absolute value of the integral is 2pi from 0 to pi.
>>
>>15129331
*infinite
*0 to 2pi
>>
>>15129331
what's your stupid question?
>>
>>15129331
It's obviously countable since there is at most n different values for this expression.
>>
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What size labcoat should I go for?
I originally had a medium sized one, and it feels burly and I feel overencumbered in it. But the wrists and arms fit perfectly.
So I am currently in the store for a small size one, this one fits my frame perfectly, but when I extend my arms the elastic cuffs pull away.
Some quick advice would be nice
>>
>>15129468
If I was doing work that required a labcoat I think I would be concerned about one that didn't cover my arms properly
>>
>>15129468
you're a homosexual pedophile who masturbates to children's cartoons
>>
>>15129481
Yes, that's what I'm mainly concerned about since I work with chemicals
But medium also feels too big. I feel heavy in it, like I need to move more than usual
>>
Is calcium bicarbonate in limestone still significantly soluble in water with a pH of 8? Building an aquarium and not finding answers nor am I a chemist.
>>
>>15129485
and this gives you power over me?
>>
>>15129490
If you're working with chemicals you're an absolute fucking retard if you're even considering working with exposed forearms and I don't understand how you wouldn't know that
Starting to suspect you're just trying to humblebrag that you're anorexic
>>
>>15129514
I'm in undergrad. They're not exposed up to my forearm anyway, and gloves cover the wrists.
>>
>>15129307
>throwing a knife
then why are knives often thrown handle first? Controlling whether it lands pointfirst is hard with primary and tertiary axis spins.
I figured since the secondary axis was so reliably unstable, throwing handle-first with a spin along the secondary axis would more reliable
>>
>>15129468
cheap polyester labcoats are flammable, so you're better off wearing cotton based shirts. If you do get the fire-retardant kind, just make sure you can tear it off at a moment's notice and there aren't any loose cuffs to drag around your workplace.
Exposed wrists aren't a problem.
>>
what math do I need to learn for biophysics and molecular biology?
>>
>>15129664
probably the same all physics students have to learn: Analysis I - III and linear algebra I - II
>>
>>15129569
>throwing handle-first with a spin along the secondary axis would more reliable
would you mind drawing a picture of what you think that would look like?
>>
>>15129664
>biophysics
non-linear dynamics and shit
>>
>>15129866
>>15129664
I see. Thank you my niggas. Any good recommendations to get started?
>>
>>15129964
I am not a physics student, but prof Leonard on youtube is good for basic calculus and learning triple integrals etc.

As for proofs, all I can say is; keep at it and try to understand/learn basic boolean logic.
>>
>>15129964
Argyris, Faust, Haase, Friedrich - An Exploration of Dynamical Systems and Chaos
is pretty good
>>
i want to learn calculus so i'm going through precalc on khan to prepare
all of it has been really easy but i got to matrices and it's a little more difficult now (linear transformations) but not impossible but my question is is the stuff at this point really necessary for calculus?
i did some googling and it looked like it's necessary for linear algebra but idk if it's that important for calculus
>>
>>15130835
Depends on how far into calculus you want to go.
If you want to eventually get to things like vector calculus or differential equations, they're very important.
But if you just want to learn basic high school level stuff? No.
>>
doesnt einsteins thery prove meth provents aging?
>>
>>15130855
alright thanks
i'll just start their calculus material and work on the matrix stuff on the side
for anyone curious heres some of the matrix stuff they have part of their precalc course
>Using matrices to transform the plane
>Transforming 3D and 4D vectors with matrices
>Multiplying matrices by matrices
>Properties of matrix multiplication
>Representing systems of equations with matrices
>Introduction to matrix inverses
>Finding inverses of 2x2 matrices
>Solving linear systems with matrices
>>
>>15128726
Me on the left.
>>
>>15128726
Cute and bunny
>>
>A logic is always a logic over a type theory
How so?
>>
>>15129279
Yes.
>>
What's the motivation behind the definition of geodesics in metric spaces? What's the benefit in studying "local distance minimizers" (= geodesics) rather than "global distance minimizers" (= shortest paths)?
>>
How much chem do I need for an intro material science class? It’s been a while since I’ve taken any…
>>
>>15131374
Because you get the same answer. Add up a series a local shortest paths and you get a global shortest path.
>>
>>15131440
But anon, let me quote the ultimate source of knowledge, Wikipedia:
>In general, geodesics are not the same as "shortest curves" between two points, though the two concepts are closely related. (...) Going the "long way round" on a great circle between two points on a sphere is a geodesic but not the shortest path between the points.
>>
>>15131459
In that particular geometry you can have two valid geodesics between two points. Clearly one will be shorter than the other and will be your shortest path.
>>
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is it doable to learn calc I + II in a month as a midwit?
>>
>>15131625
yeah
https://youtube.com/watch?v=kuOxDh3egN0
>>
>>15131701
thanks anon!
>>
Is it possible to derive joint distribution from marginal distribution and covariance?.
>>
Why can't an integer have infinite digits?
>>
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Hello frens. Code monkey here who last read a math/physics textbook 10 years ago.
I really want to learn Quantum Mechanics(then Quantum Computing as I'm a code monkey).
Is it possible? Which subjects should I learn first? Linear algebra? Should I relearn Classical Physics first?
>>
>>15128726
What kind of math should i learn for classical and quantum physics?
>>
>>15131875
>classical and quantum physics
You do realize that this includes pretty much all of physics, right?
>>
>>15131866
Just read Taylor's Classical Mechanics and make some video games or something. Quantum computing is a meme.
>>
>>15131859
It's part of the definition. Every integer (a single element in the set of integers) is finite. You can have an infinite number of integers larger than some arbitrary value but each one is finite.
>>
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What's the mathematics of math?
>>
>>15131879
Yes.
>>
>>15132007
Category theory
>>15132052
Category theory
>>
Why did Hitler use acetone to remove polish people?
>>
I’m pouring a glass of ice water, water goes on the ice.
water temperature is w, Ice temperature c, time to reach desired water temperature for drinking is t
For simplicity’s sake, we will just say
w + c = t
If we increase the water temperature slightly to w+1 so that it looks like
(w+1) + c = t
Will the time to reach the desired water temperature change proportionately with the increase in the temperature of the water being poured on the ice or will the slightly warmer water melt the ice faster, diluting the water with the cold ice melt water and cooling down the total temperature at a faster rate?
Assume that the temperature of the water being poured is below room temperature, this is not hot water, the ice is capable of cooling the water to the desired temperature
>>
>>15131625
>>15131701
>calc I + II
What's the scope of this?
>>
>>15132494
1 is differential calc, 2 is integral, usually. also some stuff about limits and series.
>>
Why are we allowed to use Mertens' theorem for the first part? Doesn't that only apply if we know one of the series converges absolutely?
>>
>>15132696
>Doesn't that only apply if we know one of the series converges absolutely?
https://math.stackexchange.com/questions/3547220/why-does-a-power-series-converge-absolutely-within-the-radius-of-convergence-usi
Very classical result but I'm unsurprised you don't know about it.

Btw what's Merten's theorem again?
>>
Is it possible to estimate or at least compare the Shannon entropy of an object or animal?
I'd like to know as I'm developing a schizophrenic theory that has entropy as the token of currency
>>
My mother did not vaccinate me when I was young, is it too late to get the vaccines now? I want to become autistic too.
>>
>>15133417
You can still get vaccinated, but it's too late to join the cool kids club. Sorry not sorry n0rmalfag ;-)
>>
>>15128726
Aspirin reduces inflammation is it a safe assumption that taking at least one aspirin a day low dosage of course would be a good counter for the chronic inflammation brought on by western society diet and chemicals? Would it also be safe to assume a dramatic upswing in health and well being in response?
>>
I'm sharing a bedroom with 6 people and I'm trying to figure out if we're legally overcrowded. By law, we have to have at least 2630 cubic feet of airspace in the bedroom. If the ceiling is a standard height, let's say 8 feet, what would the square footage have to be?
I don't have a ruler so I can't just measure my room.
>>
>>15133670
18x18 for the floor space, right? Now how do I figure out if we have that much cuz I don't hab a ruler
>>
>>15128726
how would i go about proving that the linear transformation [math]f(x,y)=(\frac{4x+3y}{5}, \frac{3x-4y}{5})[/math] is a linear isometry?
>>
>>15133670
>>15133673
Take 2630 and divide by 8 ft if you have a standard
ceiling height. So you must have at least 328.75
square feet of floorspace or roughly 18ft, 1.5in
square. You need to do floorspace differently
if it's not a square.
>>
>>15133673
Find something with a length that you know, or
run out and purchase a ruler or measuring tape.
>>
>>15133743
Just calculate that
[eqn] \| f(x,y) \|_{L^2}^2 = \|(x,y)\|_{L^2}^2 = x^2 + y^2[/eqn]
for all [math](x,y) \in \mathbb{R}^2[/math].
>>
What is the probability that three independent trivariate standard normal vectors span a subspace of dimension 3?
>>
>>15133743
Either do what the other anon said or write it out as a matrix and check the condition [math]AA^T = I[/math]
>>
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Can there be a real parameter [math]p[/math] and (not necessarily square) matrix [math]M[/math] such that all of the following are satisfied?
> All matrix entries are bounded by [math]0\leq M_{ij}\leq p[/math]
> For every row [math]i[/math], [math]\sum_{j}M_{ij}=1[/math] (so [math]M[/math] is a probability matrix)
> For every column [math]j[/math], [math]M_{ij}=0[/math] for at least [math]p\times 100\%[/math] of the [math]i[/math]'s (a kind of sparsity condition)
I suspect that the answer is no, but I haven't been able to come up with a proof or a counterexample.
>>
>>15134042
0.5 0.0 0.0 0.5 0.0 0.0
0.0 0.5 0.0 0.0 0.5 0.0
0.0 0.0 0.5 0.0 0.0 0.5
>>
Let L be the endomorphism defined this way:
[math] L: R^3 \rightarrow R^3 \\ L(1,0,2)=(1,0,2)\\L(1,1,0) = (1,1,0)\\L(1,0,1)=(0,0,0) [/math]
determine if it's orthogonally diagonalizable.

Alright so what I did was find the matrix that represents L using an orthonormal basis (I chose the canonical basis for ease of calculations), found the eigenvectors of my newfound matrix and checked if they were orthogonal (which would imply that the endomorphism is orthogonal)

when i was done i realized that the eigenvectors were the same as the starting vectors (1,0,2), (1,1,0), (1,0,1) and felt like a retard because i could have just checked if they were orthogonal, but why is this? Why are the starting vectors eigenvectors of the endomorphism represented in an orthonormal basis? i dont get it
>>
>>15131746
Not the covariance, but you can derive the joint distribution from the marginals and a so-called "copula" distribution:
https://en.wikipedia.org/wiki/Copula_(probability_theory)
The key tool is the probability integral transform, and the key result is Sklar's theorem (both discussed in the wiki page).

>>15134309
Isn't it simply that [math]L(x)=x \implies[/math] x is an eigenvector with eigenvalue 1?
(Assuming that L(1,0,1)=(0,0,0) is a typo, and that you meant to write L(1,0,1)=(1,0,1).)
>>
>>15134324
no there are no typos i meant that the vector (1,0,1) goes into the zero vector
>>
>>15134327
Right, well in that case then (1,0,1) should still be an eigenvector with eigenvalue 0.
And since your starting vectors form a basis for [math]R^3[/math] (they'd have to be, in order for L to be well-defined given those three vectors), it seems like the answer to your question is simply "the definition provided for your endomorphism is already of the form [math]L(x_i)=\lambda_i x_i[/math], so if you spot this, then you can read off the eigenbasis directly".
>>
>>15134349
i think i get it now, thanks
>>
>>15134309
An endomorphism in general has infinitely many distinct eigenbases. A single eigenbasis not being orthonormal does not imply that no orthonormal eigenbasis exist. You have to check all of them.
For example consider the endomorphism [eqn]T: \mathbb{R}^3 \to \mathbb{R}^3 \\
(x,y,z) \mapsto (x,y,0) [/eqn]

[math]\{e_1, e_2 , e_3\} [/math] would be an orthonormal eigenbasis of [math]T[/math] but [math]\{e_1, e_1 + e_2 , e_3 \} [/math] is another eigenbasis of [math]T[/math] which is not orthonormal.
>>
[math]f:[1,4] \to \mathbb{R}[/math] is continuous and [math]8f(1) = f(4)[/math]. Prove that there exists [math]x \in [1,2] [/math] such that [math] 2^xf(x) = f(2x)[/math]
I have been trying to play with some functions like [math]g(x) = f(x) + f(2x)[/math] but I can't solve this. Any hints?
>>
>>15134396
The obvious choice for [math]g[/math] would be
[math]g(x) = 2^x f(x) - f(2x)[/math]
It's continuous since [math]f[/math] is.
[math]g(1) = 2 f(1) - f(2)[/math]
[math]g(2) = 4 f(2) - f(4) = 4 f(2) - 8 f(1) = -4 g(1) [/math]

So [math]g(1)[/math] and [math]g(2)[/math] have opposite sign. Now use IVT.
>>
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>>15134408
Ahhh, I actually understand what I'm supposed to do now. Thank you.
>>
>>15133417
>My mother did not vaccinate me when I was young
like, for anything? not meningitis? thats a serious problem, anon. meningitis isnt the fuckin flu, that shit will kill you slowly and painfully.
>>
Let [math]R_\leq2[x][/math] be the space of real coefficients polynomials. Consider the endomorphism defined as follows:
[math]L(x^2)=x+x^2 \\L(x) = x^2+1 \\L(1)=x+x^2[/math]

Consider U = the subset of all polynomials with degree <=2 such that p(1) = 0;

Question: find the dimension of U and of L(U)
Answers: 2 and 1
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>>15134609
Those answers are correct if this is what you're asking.
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>>15134617
No I'm asking how to get those answers, I don't get where they come from
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>>15134624
Find a basis for U and then calculate the image of both base vectors to see that they are multiples of each other.
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>>15134625
Im not entirely sure of what i just did but i found that a basis for U is [math]Span(x^2-x),(x^2-1)[/math]
therefore L(U) = [math](L(x^2-x),L(x^2-1)) = (L(x^2)-L(x),L(x^2)-L(1))=(x-1,0)[/math] which has a dimension of 1

the results do check out but I did some weird stuff to get the basis for U and im not sure if it's justifiable. It just confuses me a lot when the exercises aren't about "regular" vector space but instead about the polynomial vector space or whatever else even though i know it's the same thing technically
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>>15134638
[math] L(U) = (L(x^2-x),L(x^2-1)) = (L(x^2)-L(x),L(x^2)-L(1))=(x-1,0) [/math]
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I don't know how proofs work
I am absolutely getting filtered, is there a video I can watch that simplifies the process to a minimum?
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>>15134609
[math] U \subseteq \mathcal{P}_n(\mathbb{R}),\: p(x) \in \mathcal{P}_n(\mathbb{R})
\\
\text{deg}(p(x))+1 \le \text{dim}(\mathcal{P}_n(\mathbb{R}))
\\
p(\lambda) = 0 \ \; \ \; \text{iff} \ \; \exists \ p(x)=(x-\lambda)q(x),
\text{ where } q(x) \in \mathcal{P}_{n-1}(\mathbb{R}) \text{ .} [/math]

so U would be the subset where elements are p(x) iff p(x) = (x-1)q(x), and p(1) = 0 means that
there is a polynomial p(x) in U with which x^2-1 or x-1 is the chosen basis.
these are deg 2 and deg 1 but both only have dim 2.

honestly though fuck this.
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>>15134654
>how proofs work
You are trying to show that one fact follows from a set of assumptions (axioms). It's just simple a priori deduction.
Read Terence Tao's Analysis.
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>>15132290
>temperature... w, .. temperature c, time ... t
>w + c = t
Didn't you learn about units? Your equation doesn't make any sense.

If you want to find out what is proportional to what, see if you can make a quantity that has proper units for time out of those temperatures and dimensionful quantities like the heat capacity and latent heat of water.
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can you have a asymmetric graph with infinite nodes and edges?
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I can't find a definition for the lifetime of an electronic state. I suppose it would be something like:
>the lifetime of an electronic state is the time it takes for the population of that state to decrease of about 68%
But what if the excited state can hold only two electrons? This definition would stop making sense
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I'm trying to calculate the number of 4-letter strings that can be made from an n-letter alphabet, if we also require each string to have at least one repeated letter.

I'm getting n^3 * 6 :
- a factor of n^2 for the not necessarily repeated slots,
- a factor of n for the two guaranteed repeated slots,
- factor of 6 = ( 4 choose 2 ) , for the ways of choosing 2 out of 4 slots , as the guaranteed repeated slots.

But this doesn't seem right, since it should be less than n^4 , but isn't when n < 6 . Can anyone help explain where my reasoning is flawed?
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>>15135201
Sure.
Define a graph where the vertices are the natural numbers and there's an edge between [math]n < m[/math] if and only if [math]\sum_{k = 1}^n k < m \leq \sum_{k = 1}^{n + 1} k[/math]
No symmetries because all of the vertices have different degrees.
>>15135267
Your entire logic is weird tbqh.
Count the complement.
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>>15135267
That'll be the number of permutations where you allow repetitions minus the number of permutations with no repetitions.

So [math]n^r - \frac{n!}{(n - r)!}[/math] where r = 4.
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>>15135275
>Count the complement.
Oops yeah, I see now
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got filtered by the second paragraph on the wiki
>The application of math in any field is considered a specialization which requires a significant amount of skill to which contemporary cultures try to measure. While math is commonly used in scientific fields, it is not a subset of them. In fact, the application of math to scientific fields is generally considered THE advancement of science. Unfortunately, due to this schism between what math is predicated on (formal logic) and what common language is predicated on (reality), the study of math for any scientific field is considered distinct and being less emphasized in education
am i supposed to understand what the fuck this means
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>>15135275
>Sure.
ok thanks because i asked the ai eight times and it said no six times, and started going on about it needing to be homogenous and that means it symmetrical. i won't trust that thing any more.
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Would it be inadvisable to spend 13 hours learning something I really enjoy, as opposed to only 3 hours of something I really enjoy? There must be a point or a range where it's not beneficial for a person to study any more in a day.

I'm not a scientist, and my googlefu is probably influenced by that, so I thought I'd ask here.
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>>15135384
>am i supposed to understand what the fuck this means
Yes. You either have low English language ability, low cognitive ability, or both.
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>>15134324
>copula
Nice thank you.
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>>15128726
When they say fusion reactions can be calculated as energy with e=mc^2, why is it necessarily squared? Would we even be able to test anything at lightspeed squared?
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>>15128726
You just know
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what is the intuition behind the first fundamental theorem of calculus? I mean I understand every step of the proof but at the end it feels like they pulled a wizard trick on me to convince me that the integral from a to b of f is F(b)-F(a) where F is a primitive
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>>15136110
The logic is that you prove that the function which literally measures the area

F(x) = integral of f from a to x

is a primitive to f, that can be easily seen even geometrically. Then you use the fact that primitives differ by a constant THEREFORE the area measuring function can be found by computing the antiderivative up to a constant. This constant is suppressed when you take the difference.
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Unzicker gets hate from reddit. Why is this?
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what happens here? I don't get it. Is there a rule that you can do this?
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>>15136193
Set "n + 1" to 2 or 3 and go through the expression step by step. If you want you can then prove it by induction. Unfortunately, there's no general rule for it that I'm aware of.
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According to Pythagoras' theorem:
[math] | \vec x + \vec y|^2 = | \vec x |^2 + |\vec y|^2 [/math]
But
[math] | \vec x + \vec y |^2 = \sum (x_i + y_i)^2 \neq \sum x_i^2 + \sum y_i^2 = | \vec x |^2 + |\vec y|^2 [/math]
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>>15136213
>According to Pythagoras' theorem
wrong
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Hey guys, what am I doing wrong here?
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>>15136213
>According to Pythagoras' theorem
Only true if x and y are orthogonal. That is, [math]\sum x_iy_i = 0[/math]. Then, [math]|\vec{x}+\vec{y}|^2 = \sum(x_i+y_i)^2 = \sum x_i^2 + \sum y^2_i + 2\sum x_iy_i = \sum x_i^2 + \sum y_i^2 = |\vec{x}|^2 + |\vec{y}|^2[/math]
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>>15128726
Do I have to use the Archimedean property and triangle inequality throughout all Real Analysis?
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did women evolve high pitched voices so that nagging is more effective?
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>>15136246
Your handwriting is fucking abysmal.
Improve it.
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>>15136193
>what happens here?
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When do we use non-homogeneous/inhomogeneous/heterogeneous as the opposite of homogeneous? It doesn't seem consistent.
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>>15136509
homo means the same
hetero means different
they are exact negations of themselves, ie let x be an object. then x is homogeneous iff x is not heterogeneous
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>>15136516
I know they're technically the same, but in practice regardless of scientific context, they're never used interchangably.
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I was able to pass calc 1 and now am taking calc 2, on the first day the teach made sure to say that we needed to have a god grasp on u substituting something I never rarely understood.

I understand making part of the promelem into u and then taking the derivatice. But why does the dx pop up, what exactly does du and dx mean. As far as I can tell they equal zero since they just disappear when convienet. Also why can you just take 1/4 out of the intergral without changing it at all.
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>>15136535
u-sub is chain rule in reverse.
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>>15136337
aha thank you
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>>15136161
he's a closeted anti-science chud
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scientifically speaking, how can I give myself erectile dysfunction?
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[math]|M| > \infty \implies [\exists\, (f_{n}: M \to \mathbb{R})_{n \in \mathbb{N}}: f_{n}\ converge\ pointwise,\ but\ do\ not\ converge\ uniformly][/math]

I want to show this by
>extract countably infinite subset of M, called it M' (<- do I need the axiom of choice for this?)
>construct a bijection g. M -> N with N being the natural numbers
>sort M' with the canonical ordering relation "<", such that (f(m1) = 1, f(m2) = 2,...)
>define
[math]f \circ g: M \ni m \mapsto \begin{cases}e^{g(m)}& m \in M' \\ 0 & m \notin M' \end{cases} \in \mathbb{R}[/math]
>the function "f combined with g" would then converge pointwise but not uniformly

Would this work?
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>>15135249
Any physicist pls?
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I'm reading Shankar's QM book and I'm already confused on page 2. He says

A linear vector space V is a collection of objects |1>, |2>, ...., |V>, ... , |W>, called vectors

My questions are:

Why does it start with |1> ?
Do vector spaces always starts with |1>?
I think this is Dirac notation but the book didn't mention it prior to starting the chapter so I'm confused
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>>15136585
I forgot to mention that divide by n in N with each step in the sequence, so that it really converges pointwise towards the constant zero polynominal
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>>15136636
It's just a convention. A different author might do things differently. Just read on.
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>>15135249
It's the time it takes for there to be a 68% chance that the electron has decayed to a lower state.
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>>15136636
> I think this is Dirac notation
It is but the author is assuming you don't know about that yet. I guess he's trying to get the reader familiar with some notation before getting into the details about what those objects represent (in QM).
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>>15136636
The basis can be labeled by anything, the labels don’t matter
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>>15136692
Oh ok, that can make sense. So then to measure the lifetime of an electronic state containing only a few electrons one would need to average over a large number of atoms, or replicate the experiment on a single atoms many times, right?
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>>15136585
>>15136639
>>extract countably infinite subset of M, called it M' (<- do I need the axiom of choice for this?)
You do, yeah.

The proof works in principle but the writing is a bit awkward. You'd usually present it like this:
>we can choose a countable infinite subset of M
>hence we only need to prove the theorem for the naturals
>here's a proof for the naturals

Also
>>sort M' with the canonical ordering relation "<", such that (f(m1) = 1, f(m2) = 2,...)
Irrelevant and nonsensical.
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>>15136902
very good, thank I'll do it like this
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is there any real world application for set theory?
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>>15136902
what's your take on this, if I may ask?
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>>15136975
The counterexample makes sense as the problem is written but if you add in the caveat that all the [math]W_i[/math] are independent the result becomes true.
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>>15137008
finally someone who understood this. Thank you
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If you were in a submersible on the ocean floor, then quickly ascended, there would be no dangers associated with decompression sickness, correct? All that matters is that the pressure vessel is strong enough, right?
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>>15137201
>not understanding that giga chad fucks the ice maid every night so hard that she has stimulated uterually induced hyper intelligence.
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>>15137213
who are you quoting?
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>>15137223
the guy above doesn't understand that ice maids intelligence varies due to being raild.
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Does environment make it more likely that a particular mutation or evolution will happen/appear compared to some other mutation?
I'm thinking about events like ability to digest milk (or lactose precisely) as adults or lack of ability to synthesize vitamin C.
According to the evolution these changes somehow make an individual to undergo such mutation to have reproductive edge over others and people who do not have such mutation will slowly die out in a mysterious manner.

So we have a prehistoric group of lactose intolerant people and they start drinking milk for some reason even if it makes them feel bad.
Is it likely that multiple people or their offspring will respond to this stimulus and develop ability to digest milk instead of just a mysterious single superman outliving everyone else and spreading his seed?
Is the chance to evolve to be able to digest milk the same in this population compared to some other where milk isn't consumed at all?
According to the gene drift, is it entirely possible that a population that never consumed milk as adults would end up as a whole with the ability to digest lactose?
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>>15137160
if the inside of the submersible was initially at 1 atm, and remained at 1 atm during the entire ascent, then yea there would be no danger. is this actually how submersibles operate? probably not if i had to guess.
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>>15137272
>Is it likely that multiple people or their offspring will respond to this stimulus and develop ability to digest milk instead of just a mysterious single superman outliving everyone else and spreading his seed?
It depends on the specifics of the stimulus. Looking it up, there are a few proposed stimuli, varying depending upon the specific region, but most seem like pretty good things for a community to follow. Stuff like "it's less likely to give you cholera than your shithole water" and "it's nutritious and you're going through your usual winter famine".
>Is the chance to evolve to be able to digest milk the same in this population compared to some other where milk isn't consumed at all?
>According to the gene drift, is it entirely possible that a population that never consumed milk as adults would end up as a whole with the ability to digest lactose?
Naturally, the odds are greater with the stimulus at play, but in theory there's nothing stopping it from happening entirely by coincidence.
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>>15137279
I know that many underwater structures increase the pressure inside, and occupants are essentially saturation diving. But even then if it ascended you'd only be in danger if you suddenly left the vessel after surfacing, without decompressing.
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Given the equation of the conic [math] A:= \{x \in \mathbb R^2 \mid 3x_{1}^2 -2x_{1}x_{2}+3x_{2}^2-32=0 \} [/math].

Find a basis for [math] \mathbb R^2 [/math] so the equation [math] A [/math] in the new basis can be [math] \frac{a_{1}^2} {4} + \frac{a_{2}^2} {2} =1 [/math]

(Let [math] a [/math] be the coordinate vector of [math]x [/math] in the new basis).
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>>15137328
why don't you just show me the answer to the questionyou just pulledout out of your LA text book?
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>>15137328
Find an orthonormal basis of the symmetric 2x2 matrix of coefficients. If the two eigenvalues are distinct then the eigenvectors will already be orthogonal; otherwise use Gram-Schmidt.
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There's a drawer with an infinite amount of socks. 10% are red and 90% are black. If I take ten socks out without looking, what are the odds that I pull out at least one red sock?
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>>15106334
Paracetamol is the brand name for Acetaminophen and it only has the effects of reducing fevers and pain relief while avoiding side effects of Ibuprofen use (increased risk of GI irritation and bleeds).
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>>15137493
Both paracetamol and acetaminophen are generic names. The name acetaminophen is used in half a dozen countries, including the US. Paracetamol is used everywhere else.

https://en.wikipedia.org/wiki/Paracetamol#Naming
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>>15137328
[eqn]\begin{pmatrix} x1 \\ x2 \end{pmatrix} = \begin{pmatrix} 2 \sqrt 2 & -2 \sqrt 2 \\ \sqrt 2 & \sqrt 2 \end{pmatrix} \begin{pmatrix} a1 \\ a2 \end{pmatrix}[/eqn]
Conversely
[eqn] \begin{pmatrix} a1 \\ a2 \end{pmatrix} = \begin{pmatrix} \frac 1 {4 \sqrt 2} & \frac 1 {2 \sqrt 2} \\ -\frac 1 {4 \sqrt 2} & \frac 1 {2 \sqrt 2} \end{pmatrix} \begin{pmatrix} x1 \\ x2 \end{pmatrix}[/eqn]
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>>15136547
I should add that the double sum can also be justified in a more "formal" manner: define an indicator function
[eqn]I(j,\nu) = 1\text{ if }j\geq\nu\text{, else }0[/eqn]
which I will also write as [math]I(j,\nu) = [j\geq\nu][/math] following the style of picrelated. Then
[eqn]\sum_{j=0}^{k+1}\sum_{\nu=0}^j S(j,\nu) = \sum_{j=0}^{k+1}\sum_{\nu=0}^{k+1} [\nu\leq j] \cdot S(j,\nu) = \sum_{\nu=0}^{k+1}\sum_{j=0}^{k+1} [j\geq\nu] \cdot S(j,\nu) = \sum_{\nu=0}^{k+1} \sum_{j=\nu}^{k+1} S(j,\nu)[/eqn]
Of course this is really saying the same thing as >>15136337, but you might prefer this "algebraic" approach over requiring some kind of "geometric" intuition.
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>>15136535
[eqn]\int f(x) \, dx = \int f(a) \frac {dx} {da} \, da[/eqn]

Informally, dx = dx/da da, i.e. you can treat dx and da as terms and dx/da as a ratio. You can't treat them as zero because => dx/da = 0/0 = undefined.

> Also why can you just take 1/4 out of the intergral without changing it at all.

Integration is a linear operation.

[eqn]\int k \, f(x) \, dx = k \, \int f(x) \, dx[/eqn]
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>>15137482
Big hint: find the probability that you pull out all black socks, and then take 1 minus that.
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>>15136571
scientifically speaking, why was my question ignored?
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>>15128726
Best way to remove Potassium Permanganate stain on my bathtub?
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>>15137201
>Sometimes I see the ice maid doing advanced math.
No you don't.
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>>15136571
wait until ur 60 years old
>>15138478
i didn't know the answer back when i was still young
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>>15137612
this is an elegant solution
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>>15138836
Nice middle school algebra bro
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I want to show that all functions f: R -> R have a attribute (A). Does ist suffice to show that all functions f: ]0, 1[ -> R have attribute (A)? I think yes, because there is a bijection between R and ]0, 1[, but I'm not sure.
>>
>Stayed up all night 2 days ago
>Slept 16 hours last night
Am I good now?
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>>15139091
No. Not all attributes of functions are being preserved when the function is being concatenated to another function.
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What is the signature of the universe?
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>>15128726
Can I tongue OP's anus if I'm not black?
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Let R be a commutative ring which is not a field. Suppose that for every element x∈R which is not a unit, we have x^2=x. Prove that for every element r∈R we have r^2=r
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>>15128726
Is an attracting fixed point the same thing as a sink? Is a repelling fixed point the same thing as a source?
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>>15139897
If the ring is not a field it has some non-unit [math]x[/math] such that [math]x \neq 0[/math]. Then, for any natural number [math]n[/math], we know that [math]2x[/math] isn't a unit either, hence [math]2^2 x^2= 2x^2[/math], and by subtracting [math]2x[/math] from both sides we have [math]2x = 0[/math]. Hence, [math]2[/math] isn't a unit, so [math]2^2 = 2[/math] and again [math]2 = 0[/math].
Do the rest yourself.
>>15139094
No.
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>>15139957
>Then, for any natural number n
Irrelevant, my bad.
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>>15136520
non-homogeneous if it's somehow unexpected that you're dealing with something that's not homogeneous
inhomogeneous if whatever you're talking about is generally more common to be homogeneous, or if you're in a non-bio field and mean "not homogeneous" but not in a technical way
heterogeneous if it's neither of these two or if you're in a biology field where the term is more technical, i.e. genetics
>>
People who grew up in space would be taller, right? Do we know how much taller?
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>>15140256
This is the kind of answer I was looking for. Thanks!
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>>15138562
use coca-cola/vinegar
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>>15139926
yes, but none of the 3 fixed points in the lorenz attractor (your pic rel) are sources or sinks.
>>
How many ways can you rearrange an english sentence such that it's grammatically correct? Is there really no easy way other than bruteforcing with a computer?
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>>15140455
It would depend entirely on the sentence
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>>15140455
that's more of linguistical problem than a combinatorial one
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I have to show that all functions f_n: R -> R are Lipschitz-continuous. Obviously this is true, a Lipschitz-constant would be "n", for example. Do I have to show this formally or can I say this obvious and move on?
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>>15140852
>can I say this obvious and move on?
Sure, as long as you have a clear script in your head of how a proof of the statement would go.
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>>15140903
I'll write it down formalized
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>>15140972
Okay.
I imagine you're most of the way done with the exhaustion proof by now and feel that I should mention that you can write down [math]\displaystyle f_n(x) = \int_0^x n \chi_{[0, 1/n]} (t) \ dt[/math] and prove from there that [math]\displaystyle |f_n (x) - f_n (y)| = \left| \int_0^x n \chi_{[0, 1/n]} (t) \ dt - \int_0^y n \chi_{[0, 1/n]} (t) \ dt \right| = \left| \int_y^x n \chi_{[0, 1/n]} (t) \ dt \right| \leq n |x - y|[/math]
The general result, as you've probably noticed, is that integrals of bounded functions are Lipschitz.
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>>15139957
>isn’t a unit either, hence 22x2=2x2
Not going to lie, I don’t understand what’s meant by this
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>>15141090
Oh nevermind I get it
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>>15141058
I'm done proving it by exhaustion. But what does the Chi-part X[0, 1/n] of the integral mean?
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>>15141090
>>15141105
I left anon like half the work and my presentation was kind of a mess but I feel like I introduced the methods he's supposed to use well enough.
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>>15141143
Characteristic function.
[math]\chi_A (x)[/math] equals [math]1[/math] if [math]x \in A[/math] and zero otherwise.
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>>15141058
Aha. I have two more questions. Set n = 1 and x = 2. In this case, we'd have
[math]\chi: \mathbb{R} \ni t \mapsto \begin{cases}1& 0 \leq t \leq 1 \\0& t < 0\ \vee\ 1 < t\end{cases} \in \mathbb{R}[/math]
and therefore
[math]\int_{0}^{2} \chi[0, 1](t)dt = 1[/math]. Do I understand this correctly? And how do I make these cool-looking, big integrals?
>>
>>15141283
A third question: Suppose
>"Integrals of bounded functions are Lipschitz-continuous"
is true (I want to prove this separately). If I then know that function f is equal to the integral of function g and that function g is bounded, couldn't I then immediately conclude that function f has to te Lipschitz-continuous?
>>
> Determine all simple graphs G for which the adjacency matrix of G equals the incidence matrix of G (with an appropriate ordering of vertices and edges).
The 3-cycle satisfies this property, and by extension any disjoint union of distinct 3-cycles. I think that this is the only family of graphs that satisfies the property.
How do I prove that no other graphs satisfy this property? I know that in an incidence matrix, all columns have two 1's in them. For this to be equal to an adjacency matrix, it must be symmetric, so all rows have two 1's in them. Hence any graph satisfying this property must be 2-regular. The only finite 2-regular graphs are disjoint unions of cycles. In other words how do I prove that no n-cycles with n>3 satisfy this property?
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>>15141449
When I say graph, I mean simple graph*
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>>15141283
>Do I understand this correctly?
Yeah.
>how do I make these cool-looking, big integrals?
\displaystyle after [math]
>>15141323
>If I then know that function f is equal to the integral of function g and that function g is bounded, couldn't I then immediately conclude that function f has to te Lipschitz-continuous?
Yes.
The result isn't really rocket science, it's just a rewriting of "bounded derivative implies Lipschitz continuous."
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>>15128726
Bear with me because I'm an iqlet
I still don't understand why the universe is not locally real because of entangled particles' spin.
If you measure the spin of an entangled particle, imo, that just looks like a measurement of heat that you created. You aren't interacting with the other particle, instead you're just using a chosen unpredictable phenomenon to generate useless information (heat). Kinda like that gay "universe bifurcation" device on youtube.
What role does time have in the entangled particles example? Can the measurement of an entangled particle be viewed differently if the sequence of events were reversed?
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>>15141536
thank you
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>>15141675
>don't understand why the universe is not locally real because of entangled particles' spin.
It is just a terrible naming. Don't take it seriously
https://www.youtube.com/watch?v=gNAw-xXCcM8
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Is it true that [eqn] (f(x)-f(a_1))\cdot\cdot\cdot(f(x)-f(a_n)) [/eqn] differs from [eqn] f'(x)^2 [/eqn] only by a constant, where [eqn] a_1,...,a_n [/eqn] are the roots of [eqn] f'(x) [/eqn] and everything is done in [math] \mathbb{C} [/math] ?

Or does anyone know if it at least is it true for [math] f'(x) [/math] as a cubic with 3 distinct roots? Thats all i care about desu
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>>15141862
Oh, if it is relevant I should mention that [math] f(x) [/math] is an elliptic function.
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>>15141862
>>15141877

NEVERMIND. I am just retarded. Ignore this question.

Although i did find something cool in that if [eqn] f'(x)=g'(x)h'(x)\cdot\cdot\cdot z'(x) [/eqn] where [math] g,h,... [/math] are linear factors i.e. 1 root (call it [math] x_g [/math] ), then [eqn] f'(x)^2=C(g(x)-g(x_g))(h(x)-h(x_h))\cdot\cdot\cdot(z(x)-z(x_z)) [/eqn]
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>>15128726
Can I think of an ordered pair as a list? A list is just more general, right? Or is there a distinction i'm not thinking of?
>>
>>15142076
Is this a CS question? In mathematics, a set doesn't have an order, unless it's indexed
>>
>>15142087
I guess you could consider it CS question.

I read a paragraph that states the definition of graphs and directed graphs are almost identical, with the only difference being that a graph is a set of vertices and a set of edges, where each edge associated to a set of vertices {v1,v2}.

And directed graph is same except each edge associated to an ordered pair (v1,v2) of vertices.

It make me wonder if I can think of ordered pairs as a type of list. Or is that is a nonsense thing to say?
>>
>>15142173
Oh, graph theory. I don't know, anon.
>>
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>tfw spent hours trying to verify/falsify sth
>finally found a counterexample
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getting my ass kicked by compound inequalities right now i can't get a single one of these fucking things right. should i kill myself
>>
find all elements x in Z_26 s.t. x^2=1. Z_130? how do you approach this question? I know it has something to do with decomposing Z_26 into Z_2 + Z_13 and decomposing Z_130 into Z_13, Z_5, Z_2, but i am confused how u actually come up with the solutions.
>>
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Anons how does Grebennikov's insect based levitation device work?

Image from page 223
https://www.thetruthdenied.com/news/wp-content/uploads/2014/03/Grebennikov-Moy-mir.pdf

Why was his work censored so that most of the technical details were removed from the published book?
>>
>>15142355
Hint: if x^2 mod 130 is 1, it follows that x^2 is also 1 when taken mod 13, mod 5, and mod 2
>>
>>15142358
It didn't. Honestly that looks like an early photoshop, the shadows don't even match.
>>
>>15142521
There's more to it than that. I get that you're just dismissively reacting to the picture.
>>
>>15128726
Simple physics question.. So with thermodynamics and all, there is no real difference between an electric oven or any electric device energy related, right? That is, if I have some logic components run code and an electirc oven running they have equal heat output to electricity assuming the components don't melt, change form or anything. I'm curious as I live in a cold environment with almost constant heating required and relatively cheap electricity costs.

I.e do I save on electricity by turning my pc/PlayStation off?
>>
>>15142548
If they really wanted a picture to show it working they'd have taken a side shot. It's fake, move on.
>>
>>15142595
An electric oven is designed to convert as much of the electrical energy into heat as possible, a cpu is designed to do the opposite. Heat is normally wasted energy. If you ran a cpu hot enough to glow like an over it'd melt long before that.
>>
>>15142724
But the end result is electricity->heat, or am I crazy? Where else does the energy go? Who cares if 1&1 or 1^0 if the end result is heat? If I use an old computer to run pointless code or what amounts to a good-looking resistor to produce heat, what is the difference?

Asking as a humble engineer
>>
>>15142756
> Where else does the energy go?
Into switching transistor states.
>>
>>15141449
Can someone help? I believe I was wrong. I think this applies to all odd cycles, not just 3. Is it something to do with the fact that all even cycles are bipartite graphs while odd cycles are not? I don't see how this relates to the adjacency matrix. I'm stuck.
>>
How many years of autism would it take me to understand why the big bang has no center? I was interested in finding a diagram which had radial boundaries (assuming a spherical explosion, such as that of a nuclear bomb in midair) explaining what astral bodies and phenomena lay within what distance to the location of the event of the big bang, but apparently that's a completely erroneous understanding. I don't see how it's logically sound for a universe to be "expanding outwards" from nothing in particular, or at least no center.
>>
When I was younger, I never cared for math at all, and incredibly struggled with it all throughout junior high and high school. Anything I have learned has been mostly forgotten, and my level of education is probably on par with early elementary students. I somehow got into programming despite my horrible lack of math knowledge. Now that I'm a lot older, I appreciate math and all of its possibilities, but am still intimidated by it. Where should someone like me start?
>>
>>15142829
you don't need higher math for programming. Learn calculus, linear algebra and analytical geometry and you're fine
>>
>>15142762
Flip 0, flip 1 repeat. It's all just heat in the end, right? Who cares what happens in between? Even if it turns some (enegry) state of zeros and one's into another it's not like one state is worth more energy than another so the transition is just heat. If I'm wrong about this plz explain.
>>
>>15142811
Midwit here but the center of anything is like the center of whatever you want to center?? So what center of the big bang but the center of everything? I'm not familiar with what you refer to as the center of the big bang but if every particle moves from a single point it is bound to stay the same as there is a shit-ton of particles, not enough directions to matter and a max speed they can move.
>>
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I am a relative noob (just started learning calculus). I watched this video demonstrating an alternative means of determining the roots of quadratics that appears to me more intuitive, simpler, and possibly as robust as the quadratic formula.
https://www.youtube.com/watch?v=MHXO86wKeDY&t=1365
What is the benefit of the quadratic formula over this method?
I did some rudimentary investigation and found the following
>As well as being a formula that yields the zeros of any parabola, the quadratic formula can also be used to identify the axis of symmetry of the parabola, and the number of real zeros the quadratic equation contains.
Unless I'm mistaken, this simpler method does does all of these things as well.
>>
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>>15142811
You have to understand that the Universe is everything, so you can't exactly see it like a regular geometrical object. To have a center, you need boundaries and all objects need to recede from said center. But this is not true in the Universe, since it is homogeneous (cosmological principle) and all visible galaxies appear to recede from your position regardless of where you are. Meaning that a same galaxy can appear to move in two different directions depending on where you observe it from.
You also have to understand that the Universe's expansion is not expansion in a traditional way, it is the scale of the Universe which is changing overtime: all objects are moving away from each other (see gif related for an analogy).
>>
>>15143314
> appears to me more intuitive, simpler, and possibly as robust as the quadratic formula.
If you did all the substitutions and rearranging it's the same formula. It also reflects similar ideas for the cubic equation. However the quadratic is taught because it's a single equation and requires no manipulation of the terms.
>>
>>15143414
gif jumpscared me
>>
>>15143314
It's literally the exact some formula as the normal one, just dressed up slightly differently. If you simplify the expression [math]m \pm d[/math] by writing everything in terms of b' and c', and then pull a factor of 1/2 out of the square root, you get the usual quadratic formula back.

If you find this derivation more helpful than completing the square there's no harm in going with it (as long as you know how to complete square a square, because that's important)
>>
>>15136277
yes
>>
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Hello, /sqt/. My book wants me to show
>It is (f_n: R -> R) is a strictly monotonically decreasing sequence of functions. This sequence converges pointwise against a continuous function f. Then f has to be the infimum of (f_n) in the ordered space CR.

Note that the ordering relation is defined by
>Let f and g be in CR. It is f <= g, iff f(x) <= g(x) for all x in R
More descriptively, it is f <= g, iff the graph of f lies under the graph of g.

As I said, the book says this is true. But I don't think so. I found this counterexample: Define (f_n) by

[math]f_{n}: \mathbb{R} \ni x \mapsto \begin{cases} \frac{1}{x - \lceil x \rceil - (1/n)}& 2 \mid \lceil x \rceil \\ \frac{1}{-(x - \lfloor x \rfloor) - (1/n)}& 2 \nmid \lceil x \rceil\end{cases} \in \mathbb{R}[/math].

I appended the graph of f_4 in the interval [-1, 3] for reference. This sequence then converges pointwise to the function

[math]f_{n}: \mathbb{R}\backslash\mathbb{Z} \ni x \mapsto \begin{cases} \frac{1}{x - \lceil x \rceil}& 2 \mid \lceil x \rceil \\ \frac{1}{-(x - \lfloor x \rfloor)}& 2 \nmid \lceil x \rceil\end{cases} \in \mathbb{R}[/math].

Note that all f_n are in CR and strictly monotonically decreasing. Function f is continuous. However f can not be the infimum of the sequence in CR, because f is not in CR. This function is not contained in CR, because it's not defined on all of R.

What do you think of this? Am I right or did I miss sth?
>>
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>>15143754
Here's the function, it converges to. Btw., I fucked up. First it's f and not f_n and the domain of f should have been R\2*Z. Also the ceiling/flooring should have been defined more precisely. Namely
>when x in Z and x is not divisible by 2, then round down to x - 1
>when x in Z and x is divisible by 2, then don't round x
>otherwise round canonically
But, you get the idea.
>>
>>15142548
Nothing about what that anon said is dismissive.
>>
Asking to see if anyone has though of this before. I am trying to find (or prove that it cannot exist) a numerical base such that:
(1) There exists a subset of the irrational numbers that can be written in a finite sequence of symbols.
(2) Every single integer can only be written as an infinite sequence of symbols.
(3) Every real number can be written as a finite or infinite sequence of symbols.
In particular, my (stupid) question is if there exists a series [math]\sum a_n[/math] such that [math] \forall n \in \mathbb{N} a_n \in \mathbb{R} \setminus \mathbb{Q}[/math] but the series converges to an integer. I believe it should exist but I don't know any.
>>
>>15143826
Unless I'm misunderstanding what you mean, doesn't any transcendental base do this?
You can't write any rational number as a finite sum of powers of (for example) pi because that would imply pi is algebraic
>>
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>>15143826
what about sqrt(2)/2 - sqrt(2)/2 + sqrt(2)/4 - sqrt(2)/4 + sqrt(2)/8 - sqrt(2)/8 + ... = 0
>>
how do i find love? scientifically speaking of course
>>
>>15143838
This is the trivial case, it's not helpful because it will always give you 0, whereas a series that converges to a nonzero real number can converge to any real number when multiplied by a constant
>>
>>15143826
[eqn]
\sum_{n=0}^{\infty} 2 \sqrt{\pi} \int_{n}^{n+1} e^{-x^2} = 1
[/eqn]
>>
>>15143999
minor correction: should be 2/sqrt(π)
>>
>>15144015
oops, ty
>>
>>15143999
why didn't you do the "dx" at the end of the integral? How do you know that all of these numbers are actually irrational?
>>
>>15144026
>why didn't you do the "dx" at the end of the integral?
forgot, or its implied, you choose
>How do you know that all of these numbers are actually irrational?
it came to me in a dream
>>
>>15143826
>In particular, my (stupid) question is if there exists a series ∑an such that ∀n∈Nan∈R∖Q but the series converges to an integer. I believe it should exist but I don't know any.
[math]a_n = \dfrac{6}{\pi^2 n^2}[/math] since [math]\displaystyle \sum_{n = 1}^{\infty} \dfrac{1}{n^2} = \dfrac{\pi^2}{6}[/math]
>>15143999
How do you prove all of those integrals are irrational?
>>
>>15143985
>whereas a series that converges to a nonzero real number can converge to any real number when multiplied by a constant
doesn't that give you a ton of examples of the kind of series you want? take a series of rational numbers that sums to something irrational, and divide by it so you get a series of irrational numbers that sum to 1
>>
>>15144042
>How do you prove all of those integrals are irrational?
technically i dont need to prove that all of the terms are irrational, only that finitely many are rational. i believe it would also be sufficient to prove that there are infinitely many irrational terms, because then you could just group every rational term with an irrational one.
i suppose that there are many many examples of what OP is looking for.
>>
Does there exist a bijective multivariable analytic function?
>>
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is this technically correct
>>
>>15144355
has to be "=" not ":=", sorry
>>
>>15144355
Not on a set theoretic level, no
there is a trivial bijection but they're not literally the same set
>>
>>15144367
Okay. The thing is: I know that a sequence of functions (f: R -> R) converges. How can I explain that they also have to converge when defined as (f: (r, 0) in R^2 -> R)? This has to be true, but I don't know how to formally justify it.
>>
Does anyone have a good study on the novavax covid-19 shot's side effects compared to other vax's.
>>
>>15144376
the metric on R^2 d2 is a generalization of the metric on R d1. Therefore if a function converges on (R, d1), it also converges on (R, d2)
>>
>>15143754
f_n R->R does not converge pointwise to f.
f_n: R\2Z -> R converges pointwise to f.

It doesn't make sense to have pointwise convergence to something with a different domain. How can I converge to the value of f at 0 if there is no value of f at 0?
>>
>>15144070
>technically i dont need to prove that all of the terms are irrational, only that finitely many are rational.
Could you do that?
>>15144275
A multivariable analytic function [math]f: \mathbb{C}^n \to \mathbb{C}[/math]?
No.
>>
>>15144485
>Could you do that?
left as an exercise
>>
>>15144480
So in this metric space, these functions (f_n) have no limes at all? Thank you, that's very crucial information.
>>
>>15144485
Then if I widen the net to injective multivariable smooth function?
>>
>>15144513
There are no injective C^1 functions [math]f: \mathbb{R}^m \to \mathbb{R}^n[/math] for [math]m > n[/math].
>>
>>15144536
Thanks anon.
>>
>>15142595
No. Or at least, not much. All of the electricity your PC/console consumes ends up as heat. Although it might not distribute the heat as efficiently as a dedicated heater.

A fan heater where the heating element has been replaced by microchips which e.g. mine bitcoin wouldn't be any less efficient than a normal fan heater, although it would probably cost significantly more.

The only way to improve efficiency for electric heating is by using heat pumps, which move heat rather than generating it. The source of the heat doesn't have to be particularly hot (otherwise the heat would just move by itself without a heat pump); you can move heat from sub-0°C ground to a 25°C room for less energy than creating the heat.
>>
anons, what are some books that rigorously build a foundation of mathematics from the ground up.
I know elements of mathematics and principia mathematica, but what are some other ones?
>>
>>15144788
why'd you want to start mathematics from set theory?
>>
>>15143499
>>15143444
Thanks, I see that now.
>>
>>15144889
i'm not really interested in learning the maths starting from the foundation, just studying the foundation itself. so, elements of maths starting with set theory, or principia mathematica starting from mathematical logic or some other book starting with something else, i just want to see as many interpretations as i can, so i can compare them. And see the primitive notions and axioms each of them assume to be true. that's all.
>>
Let (G,+G) be an abelian group. Consider the ring [math]R_{G}[/math] whose underlying additive group is Z⊕G and the multiplication is defined by [math](n,g_{1})⋅(m,g_{2})=(nm,ng_{2}+mg_{1})[/math]. Prove that if [math]R_{G}[/math] and [math]R_{G}[/math] are isomorphic rings then G and H are isomorphic as abelian gropus.

How do you approach this question? You know an isomorphism exists between G and H as rings, and I assume you somehow use this isomorphism to define an isomorphism between G and H, but I don't see how
>>
>>15128726
Hello, I'm on my way to study NLP and NLU specifically. Usually, NLU will use some scheme for feature extraction, so I was wondering how well does a regular SVD able to extract feature in NLP? Secondly, is there a conventional method for feature extraction in NLU? Lastly, can I use something like sparse least square as a method for feature extraction? Thank you.
>>
>>15145045
What's [math]R_G[/math]'s group of units?
>>
>>15145166
1⊕G?
>>
>>15143897
Attracted a mate via showing off attributes of yourself that sexually provoke the opposite sex.
Once mate is obtained start cuddling and copulating with it to cause oxytocin to release in their brain, this will lead to pair bonding.
Once you and your mate are pair bonded you will both invest into each other, if your mate doesn't invest in you then your mate is defective and you will need to start over with a new mate, after lots of investing in one another you will start to have a higher feeling know as love.
>>
>>15145206
No but pretty close.
>>
>>15145271
can you be my mate?
>>
An n x n matrix with n different eigenvalues is always diagonalizable. Instead if it doesn't have n different eigenvalues for example it's a 3 by 3 matrix and it has 2,2,7 as its eigenvalues it means it COULD be diagonalizable but I have to check if the dimension of the eigenspace associated to each eigenvalue (= geometrical multiplicity of the eigenvalue) is equal to the algebraic multiplicity of each eigenvalue and the total sum is n.

Is this correct?
Also how does someone even come up with this anyway in the first place? I hate how all books I read just tell you what to do to check something without saying why that works
>>
>>15145318
Heh, no.
>>
>>15145336
:(
>>
>>15145324
>Is this correct?
Yes
>Also how does someone even come up with this anyway in the first place?
What diagonalizing a matrix is actually doing is performing a change of basis to a basis consisting of eigenvectors of the matrix.
Checking that all the geometric multiplicities are the correct size is checking if it's actually _possible_ to find a basis of eigenvectors. If one of the geometric multiplicities is too small, then your eigenvectors can't span the whole space.
>>
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Any chemistry anons here ? How long would it take from sodium nitrate (NaNO3) dissolved in water to turn into sodium nitrite (NaNO2). Or would it even change in the first place ? I was thinking it would be like with hydrogen peroxide which does eventualy turn into water.
>>
>>15145324
> Is this correct?
Yes. Given a nxn matrix A, if P is the matrix whose columns are eigenvectors of A and D is the diagonal matrix whose elements are eigenvalues of A, A=PDP^(-1). But for this to work, P^(-1) has to exist, so P must have n linearly-independent columns, i.e. A has to have n linearly-independent eigenvectors. If any eigenvalue has a geometric multiplicity less than its algebraic multiplicity, then A doesn't have n linearly-independent eigenvectors (the algebraic multiplicities inevitably sum to n) and so isn't diagonalisable.
>>
>>15145426
No, you need heat, check out page 10 of this. There's Gibbs free energy, so it's not going to just happen.
https://hal-ineris.archives-ouvertes.fr/ineris-01863107/document
>>
>>15145569
>>15145426
also, this
https://www.epj-n.org/articles/epjn/pdf/2016/01/epjn150072.pdf
says you could do it at 600C
>>
>>15145286
+/-1⊕G?
>>
If you are struggling with a question should you go straight to the resolution or struggle for hours on end until you figure it out yourself?
>>
What is the complement of (0,1)?
>>
>>15145865
depends on what set you are working in, the complement of (0,1) in [0,1] would be {0,1}, while the complement of (0,1) in the reals would be (-inf,0] union [1,inf)
>>
about to take calc 1 for the first time and read this online
>if I ask you to add [math]\frac{x+1}{x2-x+1} + \frac{x-1}{x2+x+1}[/math] and simplify it, can you do it on your own
>1. without needing to be reminded how to add fractions?
>2. without someone to tell you exactly what steps to take?
>3. without needing to be reminded how to factor polynomials?
>4. without doing something completely and utterly nonsensical?
>you will have no problems in calculus 1 if you answered yes to all 4. if you answered yes to less than 3, then you will probably struggle with calculus.
is this true? i keep hearing different people say calc 1 is basically just algebra and trig
>>
>>15145627
Yeah so it's not literally as easy as going "the groups of units are isomorphic and they're isomorphic to G and H hence G and H are isomorphic" BUT it's not hard to prove that the induced unit group isomorphism maps [math]1 \oplus G[/math] to [math]1 \oplus H[/math].
Hint: what are the nilpotents in [math]R_G[/math]?
>>
>>15146286
that's about right, yeah.
calc only gets difficult when it gets to the really bullshit integrals, but those won't appear in any decent introductory course on the matter
>>
>>15146287
0⊕G? And isomorphisms preserve that so we are left with two subgroups 1⊕G,
-1⊕G, which are mapped to one of 1⊕H,
-1⊕H, so they must be isomorphic? Something like that?
>>
>>15146441
[math]-1 \oplus G[/math] isn't a subgroup, but the ring isomorphism fixes [math]1 \oplus G[/math] since [math](x - 1)^2 = 0[/math] implies [math]\phi((x - 1)^2) = (\phi(x) - 1)^2 = 0[/math].
>>
>>15128726
How do I stop being verbally retarded? My vocabulary is around 2000 tops and I forget what I read all the time.
>>
What the hell is the validity of substituting [math]x(t)=x_0 e^{-i\omega t}[/math] into a differential equation for [math]x(t)[/math], where [math]x(t)[/math] is the position of a particle? How can a position (meters) be a complex number?
I know this trick works and is used all the time in physics, but is there any textbook or article that explains its legitimacy with actual mathematical rigor?
>>
does somebody know how I make quantifiers bigger and bold and how I can write the variables beneath them?
>>
>>15146816
this is how I've been doing it so far. But it looks meh
>>
>>15146716
It's just additional information about the phase and initial conditions.
If you want to measure it, you take the real part.
>>
>>15146816
>how I can write the variables beneath them?
With \limits, i.e.

\mathop{\exists}\limits_{n \in \mathbb N}
>>
>>15146962
I know, but that's not what I asked
>>
>>15146979
Yes it is
>>
>114 IQ
>now 25
>frequently got shit grades in Chemistry in school
>looking to do a degree in Chemistry with an emphasis on pharmaceuticals eventually
It's been 8 years. I like Chemistry. Can I do it or would I be wasting my time?
>>
>>15147005
My question is: what tells me that the real part of the solution of a differential equation [math] \frac{d^2x}{dt}=f(x,\frac{dx}{dt},t)[/math] solved for [math]x=x_0 e^{-i\omega t}[/math] represents the particle's position?
>>
Any good books that focus on the counting aspects of combinatorics and probability. I picked up Casella and Berger to refresh myself of probability and got filtered by some questions in the first chapter itself.
Ex.
My telephone rings 12 times each week, the calls being randomly distributed among the 7 days. What is the probability that I get at least one call each day?
>>
>>15147110
>>15146716
I feel like you're abstracting the question to the point it becomes unanswerable.
If you have a differential equation and you solve it for complex-valued functions, your real solutions are the complex-valued functions that only have real values. In particular, if [math]f[/math] being a solution implies so is [math]\overline{f}[/math] (which is usually going to be the case if all terms in your differential equation are real), and your equation is linear, then you know that the real part of [math]f[/math] is a solution since [math]Re(f) = \dfrac{f + \overline{f}}{2}[/math], a convex combination of solutions to the equation.
>>
>>15146968
thank you
>>
im looking for a sentence i read at some point that went something like "an equation in n variables describes an n-1 manifold in n-dimensional space." what is the actual way to say this?
>>
Can e^x be rational for rational nonzero x ?
>>
>>15147650
Submersion theorem / regular value theorem
At least for smooth manifolds and smooth maps
>>
>>15147856
no (Lindemann–Weierstrass theorem)
>>
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i'm getting filtered hard by this shit right now and it's making me depressed knowing there are precocious 12 year olds doing it with ease. watched the video a few times and looked at all the hints for the quiz and i'm still not getting it. please help me understand

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:modeling-with-linear-equations-and-inequalities/v/comparing-linear-rates-example
>>
>>15147891
Thanks anon
>>
Is juggling the easiest way to speed up reading and comprehension/IQ? How much juggling is enough?
feeling good. stalkers go away! rof lao
And, thank you, Jim.
>>
>>15146716
> How can a position (meters) be a complex number?
It can't. However, it can be the sum of a a complex number and its conjugate, which is real.

For a linear ODE, the general solution is ce^λt where λ is a root of the characteristic polynomial. If the coefficients of the ODE are real, then any roots are either real or occur in conjugate pairs (whose sum is real). And if the initial conditions are real, then the particular solution will be real, meaning that all terms are either real or occur in pairs with the form c1.e^(λ1.t)+c2.e^(λ2.t) where c1,c2 are conjugates and λ1,λ2 are conjugates.
>>
I saw this YouTube short, youtube.com/shorts/-8ex9XdjJdE , a few days ago and I want to know, "What would be the power of a tv signal 30 lightyears away from Earth?" Wouldn't it be a very small amount of signal power? Perhaps it's hard or nearly impossible to receive such a weak signal? I never took a physics class that goes over signal strenth in telecommunications. Does anyone mind shortly walking me through this?

I don't even know if "strength" or "power" are the right words to describe properties signals.
>>
>>15147873
cant read any of this shit but thanks
>>
>>15148380
Well, if you imagine the signal spreading out in a sphere, its intensity (power per unit area) decreases. The intensity falls off as the distance squared if the radiation is dispersed uniformly in all directions. 30 lightyears would give around 10^19 decrease in intensity. I assume it would not be receivable really, though a smarter anon should confirm this.
https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/16%3A_Electromagnetic_Waves/16.04%3A_Energy_Carried_by_Electromagnetic_Waves



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