/sqt/ Stupid Questions Thread

>How do you resolve this kind of thing programmatically?
Depends on the specific context.

through what media are gravitational waves conveyed?
Light is electromagnetic
sound uses the air
conventional waves use fluid
so what does gravity use?

>through what media are gravitational waves conveyed?
God particles

Are there different types of ribosomes?

True, true.
I just did the legwork and refactored the original calculations to either circumvent absolute values or record signs where possible, and it's working smoothly.
I thought I could be lazy by applying some math, but math has no patience for that kind of shit I guess.

anyone have a source for that article that gets posted here frequently on how colleges are teaching lower and lower level math?

Here's a proof that my brainlet brain is having trouble with.

Let [math]P[/math] be the powerset of the natural numbers. Suppose that there's a function [math]f: \mathbb{N} \to P [/math] that enumerates [math]P[/math] (in other words, a surjective function) and consider the set [math]D = \{n : n \notin f(n) \}[/math]. [math]D \in P[/math] because [math]D[/math] is a subset of the naturals. So there's some [math]d[/math] such that [math]f(d) = D[/math]. - This is the part that I don't understand - So we have, for all numbers n, [math]n \in f(d)[/math] iff [math]n \notin f(n)[/math]. Hence in particular [math]d \in f(d)[/math] iff [math]d \notin f(d)[/math]. Contradiction.

Okay I get the logic and it's hard to pinpoint exactly where I have issues with the proof but I think essentially my issue is can we really just assume that there's a diagonal set like that? It feels to me that the way we defined the diagonal set is what's contradictory in nature, not the final conclusion which is just a result of an incoherent or senseless set that we built. I know however that the theorem is true because I'm seen more straightforward and imo better worded proofs of it. Thoughts and maybe can I get a sharper equivalent proof?

Light does not use a medium.
Gravitational waves are oscillations of space time itself.

What exactly is the issue you have with the diagonal set? f maps naturals to subsets of naturals, and either the natural is mapped to a set containing it or it isn't.

Like I said it's hard to pinpoint exactly my issue, I'll tell you what I'd conclude this proof with instead and maybe you'll be able to tell better what I'm confused about

"There's no Diagonal set" because by hypothesis there is no subset of N that isn't enumerated by f(n) and the diagonal set is a subset of N.

>"There's no Diagonal set" because by hypothesis there is no subset of N that isn't enumerated by f(n) and the diagonal set is a subset of N.
This conclusion doesn't make any sense to me, the hypothesis that P is enumerable doesn't tell you anything about which naturals don't get sent to subsets containing them. Can you add more steps to explain how you come to this conclusion?

The argument is just:
Assume you have enumeration f
Consider the set D (you don't make any assumptions about D)
Since f was an enumeration there is some d mapping to D, so f(d)=D
If d is in D, then d is not in f(d)=D (by definition of D), a contradiction.
If d is not in D, then d is in f(d)=D (by definition of D), a contradiction.
Those are the only two possible cases, so the only assumption that was made must be false, i.e. P is not enumerable

Does anyone have a pdf of the answer book/instructors book for "Tutorials in Introductory Physics Homework" by McDermott? Or at least point me where to find it?

Nvm, got it now. Thanks man

how the fuck can a bunch of wires show us things like tv, games, movies, etc? it just blows my mind. i mean they are metal wires and materials in the ground and yet they are capable of doing stuff like that.

Say I had a machine that could create a gravitational singularity with infinite density. If I then moved that machine, and so moved the singularity, through space would I be opposed in the same way as I would be just moving the machinery or does the singularity have conventional inertia in the same way a conventional mass would?

>infinite density

I was under the impression that electromagnetic waves were themselves the medium, as they're just two waves bouncing off each other at right angles or something

What is love Veeky Forums?

OK I realized I made a retarded mistake, nevermind

>Say I had a machine that could create a gravitational singularity with infinite density. If I then moved that machine, and so moved the singularity, through space would I be opposed in the same way as I would be just moving the machinery or does the singularity have conventional inertia in the same way a conventional mass would?
Physics breaks down at a singularity, so no one can say whether infinite smallness or infinite density are even meaningful terms in regard to one. But total mass is all that would affect its inertia, not the density of the mass. You could theoretically squeeze a grain of sand to a density at which it would become a tiny black hole, but it would still have the mass and related properties of a grain of sand.

How do i get an arbitrarily high moment from a moment generating function without having to actually take the derivatives? Like in the third question my prof gets the 12th moment through some observation of a property of the mgf that I dont understand. I can do the first and second questions by taking the first and second derivative of the mgf. Am i just supposed to recognize a pattern or is there some general trick to this?

look at en.wikipedia.org/wiki/Moment-generating_function#Definition where you have
M_X(t) =
sum_{k=0}^\infty (t^k m_k)/k!
where m_k is the kth moment

so if
M_X(t) =
e^(3t^2)

then
M_X(t) =
sum_{k=0}^\infty (3t^2)^k / k!
[taylor expansion of e^(3t^2)]

so to find m_{12} you just match up the coefficient of t^12 as done in your image, in the taylor expansion you look at when k=6 since that gives you
3^6 t^{12} / 6!
and in the moment generating function expansion you look at k=12 since that gives you
t^{12} m_{12} / 12!
then solve for m_{12}

So, I'm trying to figure out a possible way to make liquid air in my back yard.

My idea so far:
>compress to as high a pressure as practically possible; a few thousand psi, maybe more if it can be done safely
>cool to around -40C using a modified aircon system
>expand this cool, compressed gas through a needle valve into an insulated vacuum chamber

Will the rapid expansion cause the gas to cool enough to liquefy? I know enough about air conditioning systems to make what I have in mind work, but I don't know if the science behind it is solid.

kekth'd

how do I find riemann normal coordinates around an arbitrary event?

First remember that if X >= 0, then |X| = X
and if X < 0, then |X| = -X
Rearrange your equation to get
0.001*AD = |B - C|
Then there are two cases:
If B - C >= 0, then 0.001*AD = B - C
which means that B = C + 0.001AD
Otherwise, if B - C < 0, then 0.001*AD = C - B
which means that B = C - 0.001*AD

Stats brainlet here, I feel like I must be completely misunderstanding the method of moments because I'm getting an unbiased estimator that should be biased according to the exercise (and considering the circular nature of my calculations I'm not surprised that it seems to be unbiased). Could someone point out what I'm doing wrong?

How come sometimes you have to pee really bad, but when you finally do there's a lot less than you expected?

That is some autistic writing, are those squares either those squares are 1x1cm or you can't write for shit.

Why do people write math on grid paper anyway?

The squares are exactly 1x1cm, yes. How does their size make the writing more or less autistic?

Hello.

"Given the region bounded by [math]y = x^{2}[/math] and [math]y = 1 [/math], find the volume given by a partial rotation with angle [math]\theta[/math] around x-axis".

I don't know how what the fuck I'm supposed to do now.
pls halp

The existence of set D follows from
en.wikipedia.org/wiki/Axiom_schema_of_specification

Which, in essence, says that if you have a way of assign a sentence to each element of a set A, then there exists a subset B composed of all elements for which the sentence corresponding to that element is true. In your case the sentence assigned to n is "n is not an element of f(n)".

Because it'd look more æstetic if you sized your writing accordingly to fill the entire square instead of leaving it half empty vertically, like this:

(also pls dont dox me)

I like leaving some space so I can fit taller symbols/formulas without having to either squish them down or skip entire lines.

>also pls dont dox me
maybe you shouldn't bully people on the internet

i would use a double integral in polar coordinates

I still don't know this stuff

en.wikipedia.org/wiki/Normal_coordinates#Geodesic_normal_coordinates

What's a good textbook / lecture notes to get started in tensor analysis?

Target
>brainlet electrical engineer
>already graduated so my formal "mathematical proof" skills are pretty rusted

Goals
>get an intuitive understanding about the difference between tensors and matrices
>get enough intuition so I can use this tool
>eventually understand why it's so important on the general relatively (beside ease of notation)
>if possible a book with a lot of examples / detailed exercises answers

Why is Lim h->0 (f(g(x+h))-f(g(x)))/(g(x+h)-g(x))=f'(g(x))?

Why would you try to find volumes which require double integrals in polar coordinates before learning about double integrals and polar coordinates?

What is a better way to understand Catalan numbers?

Not sure how this cipher is supposed to work. How am I supposed to get 1005036864 from 'E' XOR h? Using Python.

...

Both [math]f[/math] and [math]g[/math] need to be continuous and if the derivate of [math]f[/math] exists at [math]g(x)[/math], then it is because [math]g(x+h)[/math] approaches [math]g(x)[/math] if [math]h\to 0[/math], so you could substitute [math]g(x+h)[/math] by [math]y[/math] and [math]g(x)[/math] by [math]a[/math] and then you get [math]\lim_{y\to a}\frac{f(y)-f(a)}{y-a}=f'{a}[/math] by the definition.

[math]\lim_{y\to a}\frac{f(y)-f(a)}{y-a}=f'{a}[/math] written again

[math]\lim_{y\to a} \frac{f(y)-f(a)}{y-a} =f'(a)[/math] written correctly

How can I evaluate this integral?
[math]\int \sqrt{x^{2}+25} dx [/math]

I did the trig substitution but I got stuck at [math]25 \int sec^3{\theta} d \theta [/math]

Say I have [math]\int_0^\infty \frac{\sqrt{x}}{x^2+1}dx [/math]
I can solve this by going to the complex plane then the integral needs to be from minus infinity

[math]\int_0^\infty \frac{\sqrt{x}}{x^2+1}dx = \frac{1}{1+i}\int_{-\infty}^\infty \frac{\sqrt{x}}{x^2+1}dx [/math]

I do not see where that [math]\frac{1}{1+i}[/math] comes from.

I guess it's like the half you get when you extend an even function in this way but I just don't see how.

>Say I have [math]\int_0^\infty \frac{\sqrt{x}}{x^2+1}dx[/math]
>[math]\int_0^\infty[/math]
>[math]\infty[/math]
No you don't.

>I do not see where that 11+i comes from.
Then why do you think the equality is true?

int_{-\infty}^\infty \frac{sqrt{x}}{x^2+1}dx =
int_{-\infty}^0 \frac{sqrt{x}}{x^2+1}dx + int_0^\infty \frac{sqrt{x}}{x^2+1}dx =
-int_\infty^0 \frac{sqrt{-x}}{(-x)^2+1}dx + int_0^\infty \frac{sqrt{x}}{x^2+1}dx =
-int_\infty^0 \frac{i*sqrt{x}}{x^2+1}dx + int_0^\infty \frac{sqrt{x}}{x^2+1}dx =
int_0^\infty \frac{i*sqrt{x}}{x^2+1}dx + int_0^\infty \frac{sqrt{x}}{x^2+1}dx =
i*int_0^\infty \frac{sqrt{x}}{x^2+1}dx + int_0^\infty \frac{sqrt{x}}{x^2+1}dx =
(1+i)*int_0^\infty \frac{sqrt{x}}{x^2+1}dx

pls halp

tutorial.math.lamar.edu/Classes/CalcII/TrigSubstitutions.aspx

I saw it in a calculation that did not explain it, it was just another step.
Thank you!

i just bombed 3 exams, 2 of them in courses that are prerequisites for next semester. should i drop them and waste a year, or should i take a gamble on the final exam

Is there any similarity between the concepts of a unit root for a time series dataset, and the characteristic roots of a function?

Or are they just similar in name? They both have something to do with differential equations I think, right?

Whats the best place to learn about phasors?

My professor butchered the explanation for them and I've been left wondering what the fuck I just read.

idk visit Catalan?

Is the word "scientist" protected in any way?
If i get a Bachelor's degree in Computer Science, can i call myself a scientist?

>If i get a Bachelor's degree in Computer Science, can i call myself a scientist?
No, computer science doesn't use the scientific method.

No, just look at (((Bill Nye))) the (((Science))) Guy

Which makes it superior.

He's called the science guy because he explains science. That doesn't make him a scientist. It's like how you might call someone from the IT department of a company "the computer guy" even if he has no degree in computers

The real question is why would you want to?

I want to cosplay as Makise Kurisu from Steins;Gate (she sometimes wears a scientist costume)

My book's definition of perfect set:
closed and doesn't contain isolated points

Wikipedia's definition of perfect set:
S = closure of S

What the fuuuck {1 / n where n is natural} union {0} is closed by wikipedia's definition but that has isolated points up the ass

>n is natural
Arbitrary natural numbers need not be well-defined.

RF/Analog/Mixed signal design or photonics/optoelectronics for EE specialization if I dont plan to stay in academia after grad school? Interested in both options just need to decide on which is best for industry employment.

aRbiTrary NaTuRAl NuMbErs NEed NoT bE WelL DeFINeD

>>>/facebook/

Nvm I was being gay. Wikipedia says
S = limit points of S
not closure of S

How answer Q13?

The formula I have for the variance of a random variable is:
[math]V(X) = E(X^{2}) - E(X)^{2}[/math]

but I don't think I'm doing it correctly.

Essentially the vales I have are:
0*(1/3)
1*(2/9)
2*(4/27)
3*(8/27)

so what should the variance be, assuming X is the left-hand side of those numbers?

Whoops forgot image

What is X?

X is the probability that an email system will correctly classify an email as spam
P(correctly classify) = 2/3
P(Incorrect classify) = 1/3

babby's first algebra based physics class?

I thought this was the stupid questions board?

Pr(X=0) should be 1/27 and Pr(X=2) should be 4/9.

Var(X) should equal 2/3

Need:
The intersection of a perfect set and a compact set that is not compact.

Or need to explain why that's impossible

Well, after a bit of research, it turns out that I basically described an over-complicated version of the Linde process. This should be easier than I thought.

>autistic writing
>Because it'd look more æstetic if you sized your writing accordingly
now here's a pot calling the kettle black if I ever did see one

[math] s=\sqrt{2\cdot9.8\cdot(4\cdot s)}\cdot1+\frac{1}{2}\cdot9.8\cdot1^2 [/math]

>algebra based physics class
I wish I could turn back time
to the good old days

How to lick own butthole

I forgot to include all the details, my bad.
The system is given 3 emails to classify maximum. If it makes one wrong classification, it stops.
So the sample space I got was:
{W, RW, RRW, RRR}
Assuming W = Wrong classification and R = correct classification, and that
P(W) = 1/3
P(R) = 2/3

Or does that not change anything?

Can anyone spoonfeed on the implications of quantum wavefunction collapse?

From what I understand the consensus is that this implies pure randomness and a stochastic universe, but wouldn't it make more sense to assume that the collapse is driven by a deterministic mechanism we can't observe? Can't there be some hidden law or information that determines where the wave will collapse?

If i have two natural numbers and show that their multiple is natural by an axiom of closure of multiplication, and then expand it to a sum of 3 terms, can i conclude that ive proven thwt one of those terms is a natural number by closure of addition?

It's a dichotomy. You can have a deterministic universe, but then it is non-local. We choose the local, non-deterministic interpretation.

More here: en.wikipedia.org/wiki/Bell's_theorem