/sci/ - Science & Math

>>15034337
Is there a formula for the optimal rope length for hanging a body?

If Antares translates as "against Ares" or "anti-Mars", what would be the antonym in a Freek translation? Synares?

>>15034404
*Greek translation

>>15034337
Can someone fucking redice this?:
(sin(2a)-sin(2b))/(sin(2a)+sin(2b))
to this
tan(a-b)/tan(a+b)
.

>>15034431
double angle formula, fren

Why doesn't synthetic biology get the same hype as AI?

>>15034439
Got it down to:
(sin(x-y)cos(x+y))/(sin(x+y)cos(x-y))
but now I'm stuck again. I see a lot of people just skipping to
(sin(x-y)cos(x+y))/(sin(x+y)cos(x-y)) = tan(x-y)cot(x+y), is that a trig identity? Or am I missing an intermediate step.

Getting filtered by optics and I need to present a solution for an exercise. Getting shafted, it's 5am and I haven't slept kek. I bet "it's a trig identity" isn't gonan cut it for that last step.

>>15034485
>a lot of people
fuck I'm tired, I mean some calculators show that in the last step. But then these faggots want 3 bucks from me for the explanation kek.

>>15034485
>>15034493
nvm, I'm fucking retarded atm. It's the definition of tangent and cotangent, gonna get some sleep now anons. Thanks

Difference between the shell method washer method

Okay so for both of them I find the points of intergration by getting x. Is there a difference in how I do this. My professor in shell example sets the functions equal to each other and then factors x.
y=x^2, y^2=8x

For the washer method he solves for x,
y=x^2, y=4-x^2

But its only different because the y values are different, if you switched the sets of y values from the washer to dish you would still find the points of intergration the same way right?


And then for the formula for washers its the antiderivative of
pi * [(r1^2)-(r^2^2)
?

And for shell method its antiderivative of
2pix * (r1-r1)
So instead of squaring r1 and r2 I multiply them by x, and its always just x right that doesn't change; its never like x^2 or 2x?

And then after that I just solve

Is all that the proper method?
I still don't really get what determines whether its r1 or r2

And when is says about the y axis or about the x axis what does that mean?, what changes in the formula

>>15034702

>>15034702
The disc (washer) method splits the volume into an infinite number of thin washers (i.e. discs with holes). If you're rotating about the y axis, each disc is perpendicular to the y axis, has inner radius f(y), outer radius g(y), thickness dy; the area of the hole is πf(y)^2, the area of the disc with the hole filled in is πg(y)^2, so the "washer" has area πg(y)^2-πf(y)^2 = π(g(y)^2-f(y)^2) and volume π(g(y)^2-f(y)^2)dy. If you're rotating about the x axis, swap x and y, i.e. π(g(x)^2-f(x)^2)dx.

The cylinder (shell) method splits the volume into an infinite number of thin cylindrical shells. If you're rotating about the y axis, each shell is parallel to the y axis, has radius x, circumference 2πx, height g(x)-f(x), area 2πx(g(x)-f(x)), thickness dx and volume 2πx(g(x)-f(x))dx. If you're rotating about the x axis, swap x and y, i.e. 2πy(g(y)-f(y))dy.

It's essentially just finding a formula for the volume of each infinitesimal washer or shell then summing (i.e. integrating) them.

> y=x^2
=> y^2=x^4
> y^2=8x
=> x^4=8x
=> x=0 => y=0
or
x^3=8 => x=2 => y=4
So the points of intersection are 0,0 and 2,4.
You're rotating about the y axis. So for the cylinder method you want y as a function of x. y=x^2 is already in that form, y^2=8x => y=√(8x). So the integral is
[eqn]2 \pi \int_0^2 x \left ( \sqrt {8x} - {x^2} \right ) \,dx[/eqn]
For the disc method you want x as a function of y, so y=x^2 => x=√y, y^2=8x => x=y^2/8 and the integral is
[eqn]\pi \int_0^4 \left ( \sqrt y \right ) ^2 - \left ( \frac {y^2} 8 \right ) ^2 \,dy[/eqn]
In both cases, the result is 24π/5.

>>15034337
where is the unanswered questions list? I want remi to tell me that my question is stupid.

>>15034337
Why can't we fire all our non-biodegradable 'waste' into the sun? The best argument i can think of is that the waste will eventually evolve an ecological niche in the far future made up of organisms that consume it all. I hate whenever someone mentions costs.

>>15034873
> Why can't we fire all our non-biodegradable 'waste' into the sun?
Cost.

>>15034873
If Earth's mass is decreased and Sun's increased, wouldn't it drift further towards the sun?

>>15034894
we should launch it at the moon instead then, since it's already moving further away

>>15034873
The ecological cost of a rocket launch (using current tech) is more than that of the waste itself. Also it's very, very expensive.

>>15034792
I was sleepy when I made the new thread.
Don't worry, I'm certain your question was stupid.

>>15034792
>>15034936
No one ever answers the old questions anyway.

Why are pigs so resistant to prions? Do youkai also have a similar ability?

>>15034752
OKay that makes sense, but how do you pick which function is f(x) and which is g(x) when doing your formula

How can I show this? I can just find proof that the harmonic sum has no bounds.

>>15035184
>the harmonic sum has no bounds
Yes. To clear up some confusion: they are talking about "a harmonic sum", meaning any [math]s_n:= \sum_{x=1}^n \frac{1}{x}[/math], while "the sum" usually refers to [math]\lim_{n\to\infty } s_n[/math], which diverges.
So you'd have to show that inequality being true for any [math]x\in\mathbb{N}[/math], which you can probably do with induction.

>>15034337
Can you prove a lemma in the middle of a contradiction proof with a contradiction?

>>15035275
Of course. A lemma is an independent proof to the main theorem so can be solved using any method you want to.

>>15034938
i do sometimes, but no one ever says thanks. its hard out here.

>>15034396
Newtons 2nd and 3rd law.

>>15035123
I still don't know how to decide what function is f and which is g for the shell and the washer method,

>>15034702
This looks like the stuff I did in complex vector analysis. Never wanted to pull my hair out more than ever. When it says "about the y axis" I'm pretty sure that means the object is rotating around that axis, imagine a tire on a car, when you drive it rotates about the x axis. If you crashed and your car flipped up on the passenger side, then it would be spinning about the y axis. Good luck, fren.

>>15035123
>>15035462
f is the lower bound, g is the upper bound.

You can write the integral as |g-f| or |g^2-f^2|, in which case swapping f and g doesn't matter, but you still need to know which is greater to evaluate the |...|. You normally want the integrand to be non-negative over the entire interval of integration. If f-g changes sign at some point in the interval, unless you want a signed volume you need to split the integral at that point and swap the order.

For sufficiently small x, x^2 will always be smaller than √(kx). Likewise ky^2<y. And you're integrating from zero to the point of intersection, so whichever is smaller close to zero will be smaller over the entire interval.

Where did I fuck up

>>15035761
Take the square root out of the denominator and apply distributive property.

I’m working though Logical Methods by Roger Antonsen. The book is great, but unfortunately because it’s used for his class, answers are not available. The book covers topics like Set Theory, Propositional Logic, Relations, Proofs, Functions, Recursion, Combinatorics, Graph Theory and more. How should I go about check my answers?

>>15035327
Thanks are pretty scarce in general in these threads tbqh.
>>15035816
Go to a maths discord server (i.e. discord.com/math) and ask around if anyone's got solution sets they could share or if they could look over your proofs.

Or just post them here.

Thanks for the thread op.
This is a question about biology I didn't want to waste a thread on. Why does diarrhea burn? Google says it's because of stomach acid. Is this true? How did stomach acid and digestive enzymes get through the large and small intestines? Are they resistant? Also is it possible to shit out pure stomach acid if you eat nothing for a long time and then take a lot of powerful laxatives?

>>15035761
The equation inside the integral is
x^(1/2) + x^(-1/2)
Which evaluates to
(2/3)(x^(3/2)) + 2x^(1/2)

At 27 this is (2sqrt(729)) + 2sqrt(27))
At 1 this is 8/3.

So (2sqrt(729)) + 2sqrt(27)) - 8/3

Also what college is this? Do all colleges use the exact same math problem formatting?

>>15035761
>>15036171
So it looks like your second line doesnt make any sense. It should be

(2(x^(1/2)))(1 + (x^3)/3)

Lads, why did you not inform me that geometry is the most difficult branch of mathemaatics?

Which colour paint would keep my car colder, white or silver?

is it possible to invert this matrix in a11? If so, how?

>>15036946
it's supposed to be Zˇ11. It didn't copy properly

>>15036816
Why are you asking us stuff you can google?
https://turborevs.org.uk/best-car-paints-for-hot-weather/

Can somebody explain why I should believe the sum of all natural numbers up to infinity is -1/12, that makes no sense whatsoever.

Feels like people stare too much at the math and don't step back and ask is this actually possible because it clearly isn't.

>>15036946
>is it possible to invert this matrix in a11?
Yes since the determinant is 5.
>If so, how?
The same way as in vectorspaces over every other field. Start with
[eqn] \begin {pmatrix}1&2&3&4&5&1&0&0&0&0\\ 2&3&4&5&1&0&1&0&0&0
\\ 3&4&5&1&2&0&0&1&0&0\\ 4&5&1&2&3&0&0&0&1&0
\\ 5&1&2&3&4&0&0&0&0&1\end {pmatrix}
[/eqn]
and apply row operation until you have the identity matrix on the left. Then the entries on the right tell you the inverse of the matrix.

>>15036994
State in which *exact* context the claim that the "sum of all natural numbers up to infinity is -1/12" is made.

https://danbooru.donmai.us/posts/5327330
>this has a sensitive rating because you can see some of her bare shoulders
How do we solve the coomer problem? Do we need to just eradicate most of the male population?
>>15036405
It kind of depends on what you're good at.
I'd insist that combinatorics is harder because I fucking suck at it.

>>15036946
[eqn]
\begin{pmatrix}
7 & 5 & 5 & 5 & 3 \\
5 & 5 & 5 & 3 & 7 \\
5 & 5 & 3 & 7 & 5 \\
5 & 3 & 7 & 5 & 5 \\
3 & 7 & 5 & 5 & 5 \\
\end{pmatrix}
[/eqn]

>>15037138
that pic has a sensitive rating cuz it has a goddamn suck machine in it. and it doesnt help that kirby's in it too.

>>15037234
>While she is naturally known to drink human blood, with a particular preference for B-type blood, her light appetite means her victims rarely die from their wounds. However, since she tends to stain her clothes a deep scarlet from the blood, she is also known to be called the Scarlet Devil (Akai akuma).
Not really what you'd call a highly effective suck machine.

>>15034337
---
A car starts braking, with x_0 = 0 and v_0 = 40 m/s at t = 0. Let [math]\mu[/math] be the static coefficient of friction.

Calculate the time it takes to brake when the car went v_0 upon braking and then calculate the distance traveled when the car started braking.
---
How the fuck do I solve this? So I started with this (it's correct, question was lead in this form):
[math] m \dfrac{d^2x}{dt^2} = F_{brake} \Leftrightarrow m\dfrac{d^2x}{dt^2} = -\mu mg \Leftrightarrow \dfrac{d^2x}{dt^2} = -\mu g [/math]

But now I'm stuck, do I just treat g as a constant or do I solve a diffeq here? And how the fuck do I solve this without knowing the static coefficient of friction.
---
Fuck, I dropped some courses and am a bit behind in physics, have to get up to speed. again

>>15037579
>But now I'm stuck, do I just treat g as a constant or do I solve a diffeq here?
[math]g[/math] is the Earth's acceleration, it's a constant.
>And how the fuck do I solve this without knowing the static coefficient of friction.
If you're expected to give numeric results, then yeah, you'll need the coefficient since both the braking time and distance depend on it.

Is linear algebra a meme?

In what way does it affect me as a frontend web dev?

>>15037595
Odd. The static coefficient of friction isn't given, but the original question states:
a) Derive an equation of motion x(t).
b) Calculate the braking time when v_0 = 40 m/s and then calculate the distance traveled.
We are only given:
[math] m\dfrac{d^2x}{dt^2} = F_{brake}[/math]

Read it over multiple times. I had integrated the LHS and RHS twice to get:
[math] x(t) = - \dfrac{1}{2} \mu gt^2 + v_0t [/math]
Sounds odd to give a question with an exact velocity then expect variables back for an answer. The question should be small, since it gives very little points (relatively) compared to other exercises in my problem set.

>>15034337
I need help with a simple question about matrices. I even LaTeX'd it up for y'all. https://mathb.in/73498

>>15037625
You plugged in [math]x'[/math] at [math]x[/math], which is backwards (and similarly for [math]y[/math] but if I kept mentioning it the post would be really long).
Either you calculate [math]x[/math] in terms of [math]x'[/math] and replace it in [math]y = 2/x[/math] or you calculate [math]x'[/math] in terms of [math]x[/math] (which is what you did) and replace it in [math]x'^2 - y'^2 = 4[/math]

>doing process where i have to bake at 190 C then again at 90 C
>have to wait for hotplate to cool down
>spray IPA all over it
>works like a charm
>do this for several weeks
>friend catches me doing it
>yells at me and calls me retarded
the hotplate is an a fume hood, so it really isnt a big deal right?

>>15037670
Thank you for the help!

I plugged the substitutions for [math]x'[/math] and [math]y'[/math] into [math]x'^{2} - y'^{2} = 4[/math] to get [math]y = 2/x[/math], but I'm having trouble doing it in the other (more natural) direction, presumably because I can't isolate [math]x[/math] purely in terms of [math]x'[/math] (and the same argument with [math]y[/math], but for brevity I focus on [math]x[/math]), there's some nagging [math]y[/math], and whenever I plug [math]2/x[/math] in its place, it just gets worse.

What am I doing wrong?

>>15037754
>spray IPA to cool down
Why are you spraying beer at your hotplates when you can just use cold water?

>>15037796
> but I'm having trouble doing it in the other (more natural) direction, presumably because I can't isolate x purely in terms of x′ (and the same argument with y, but for brevity I focus on x), there's some nagging y,
Use [math]R[/math] from the start of the problem.
I mean, that's how inverses work, [math]R^{-1}[/math] sends [math]x, y[/math] to [math]x', y'[/math] and [math]R[/math] sends [math]x', y'[/math] to [math]x, y[/math]

>>15037819
Thanks! Now it's crystal clear. Clearly I'm not thinking in terms of values being "sent" from one place to another, any recommendations on where to go to hone this skill? Or does it just come with time?

>>15037836
It comes with time.

>>15037754
It's a major deal. The beer contaminates the
lab equipment, or at least screws up its functions.
Your friend is right, you know.

I'm working on some group theory and could use some help with a problem.
In the group [math]\mathcal{S}_6[/math], consider the subgroup [math]H[/math] generated by the transpositions [math](1 2), (3 4), (5 6)[/math].
One of the questions is to determine the order of the normalizer [math]N(H)[/math].
I feel like I'm missing something obvious. [math]H[/math] seems to be isomorphic to [math]C_2 \times C_2 \times C_2 [/math], but I'm not sure how that helps me.

>>15038350
I haven't done group theory in a while so this might be completely retarded but isn't the order of the normalizer the order of [math]G[/math] divided by how many conjugates [math]H[/math] has in [math]G[/math]?
Which should be, combinatorially, the number of ways you can split [math]\{ 1, 2, 3, 4, 5, 6 \}[/math] into three sets with two elements each (I might be wrong but I think transpositions were only conjugate with other transpositions, which would trivialize this part).

>In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series.
i'm learning algebra 2 and using khan for questions. all the questions about "even and odd functions" are easy as fuck but can someone tell me why this matters? is knowing about this relevant for trigonometry or calculus? what are some practical applications of this knowledge? i know wikipedia mentioned "power series" and "fourier series" and i read a little about them but they didn't really help to answer my questions.

>>15038541
Yeah that's essentially what I did after a while. I wasn't sure if H has to conjugate onto another trio of transpositions, but my thinking is that every subgroup like H (just with different transpositions) has to be contained in a Sylow 2 subgroup. Those Sylow subgroups have to be unique to that transposition subgroup, otherwise that subgroup would have to have a 3-cycle in it, from which you could generate a way bigger subgroup than of order 16.
So each variant of H (of which there are 15 by my math, i.e. ways to choose three two element subsets of {1, ..., 6}) is inside a unique Sylow 2 subgroup, and Sylow 2 subgroups conjugate onto each other.
And then 6!/15 is 48, which should be the order of the normalizer.

>>15034337
Is there a way to derive the height of a pendulum given its period T and the displacement x from its origin to a point where our angle is alpha (but alpha is unknown)?

You are allowed to use small angle approximation.

>>15034337
Where do I find the Rosseland mean opacity for gaseous carbon at high temps? I need it for my senior undergrad thesis on nuclear pulse propulsion so I can calculate the ablative mass loss on the pusher plate.

>>15034337
Why is:
[math] 2sin(\dfrac{x}{2}) \approx sin(x) [/math]
a good approximation for small angles? Found it in a physics book, but no explanation was given. Calculators show it's accurate though.

>>15038616
One practical application is that if f is odd, then you know that
[eqn]\int_{-a}^a f(x) \,dx = 0[/eqn]
without needing to find the antiderivative of f.

In power series, an even function only has terms of even degree while an odd function only has terms of odd degree. In Fourier series, an even function only has cosine terms while an odd function only has sine terms (or for the complex version, the Fourier transform of a real, even function is real and even, that of a real, odd function is real and odd).

If you apply a non-linear function f to a sine wave, f(sin(ωt+φ)), you get harmonic distortion. If f is odd, you only get odd harmonics, if f is even you only get even harmonics. This follows from the fact that sin(nx) and cos(nx) expand to homogeneous degree-n polynomial in sin(x) and cos(x). The sound generated by musical instruments consists primarily of odd harmonics. Electric guitar amplifiers and distortion pedals intentionally generate even harmonics, which are characteristic of the "rock guitar" sound.

>>15038863
The important thing is [math] \sin x \approx x [/math] for small angles. The graphs of the two make it obvious why.

>>15038863 #
The important thing is [math] \sin x \approx x [/math] for small angles. The graphs of the two make it obvious why.

>>15038879
Got it, thanks anon.

I'm a couple weeks away from my senior year as an engineering major, I'm in a unique position right now. I really enjoy the subject matter of my senior level courses, but I'm not 100% sold on grad school right now, especially with the tricky financials of it. I'm not sure how worth or helpful a masters would be in the long term.
I have the potential option to do co-term to keep my undergrad aid though my fifth year, or I graduate normally and apply for grad school, and deal with whatever funny business that entails. Or, I could take classes as a non-matriculated grad student, but then I likely lose aid and I have to stay in the area of my uni. Last and most likely desu, I could just graduate and go straight into industry, but I lose out on the motivation and environment to learn more quickly in school.
Do you guys have any suggestions on what to do?

>>15038350
>>15038541
>>15038648
Uh oh mathbros...

>>15039053
>number of conjugates of [math]H[/math] in [math]S_6[/math]
There are 15, not 48.

The proof makes no sense and I have no idea why does it work. Sasuga chatgpt.

>>15038879
It's even more obvious if you look at the Taylor Series: [math]sin(x) = x - \dfrac{x^3}{3!} +\ ...[/math]

>>15039053
Eh, it's still got a long way to go.

Can someone explain what the last sentence means? Supremum should be a constant if it exists, so how can it get smaller? I am assuming
[math] \sup_m | a_m - a_{m-1} | := \sup \{ | a_m - a_{m-1} | : m \in \mathbb Z \} [/math]

how would you simulate a wave and wave-wave interaction in software? particles are easy because they're discrete, but waves aren't exactly...

>>15039565
You make them discrete. Any simulation has to run on a finite spatial grid.

If we consider the inverse of a piecewise combination of the strictly increasing functions x and x+1, then it is a piecewise combination of x and x-1, yet the latter is not strictly increasing. But inverse of increasing functions should be increasing???

>>15039593
right, but like... how? for example when you want to test 2 balls bouncing around a room for a collision, despite their position being discrete at each step, you can perform a continuous collision detection between steps, which is non-discrete, that will then yield a discrete result that you can then use to find the new positions

additionally you store these balls as positions and speed vectors, how do you store a wave?

>>15039598
There are various algorithm to do it but essentially you cut the wave or fluid into a grid or mesh of interconnected particles.

>>15039501
What it means is that if you can imagine the
"spacing" between each term of the sequence,
the supremum is the biggest spacing between
two consecutive terms at some point m.

The twist is that you need to choose a
sequence where the supremum becomes
smaller...you keep adjusting the one sequence
where each term starts closing in towards one another.

Hi /sqt/.

I got the 5-number summary of some real world dataset, aka 0th, 25th, 50th, 75th and 100th percentile of it's distribution. What would be a good way of estimating a given percentile, eg 30th from just these 5 points?
I guess I have to somehow interpolate it. I could do it linearly it probably can be done better. Maybe using a polynomial(Lagrange?) but I'm not sure if that method can't give me some absurd data(eg the resulting polynomial won't be nondecreasing like the percentile values).

Not a homework btw, this problem arises at my programming work related to finances.

>>15039627
I don't get how supremum can become smaller, what is the definition?

How do I solve
[eqn]z = \frac{\partial z}{\partial x} = \frac{\partial z}{\partial y}[/eqn]
for [math]z = f(x,y)[/math]

>>15039764
[eqn]z = \frac{\partial z}{\partial x}[/eqn]
implies that
[math]z = g(y) e^x[/math]
for some function [math]g[/math].
Now plug this into
[eqn]z = \frac{\partial z}{\partial y}[/eqn]
to see that [math]g(y) = C e^y[/math] for some constant [math]C[/math] so the solution is
[eqn]z = C e^{x+y}[/eqn]

can someone check my argument?
We say a functor [math]F:\mathcal{C}\rightarrow\mathcal{D}[/math] is an embedding if [math]F[/math] is injective on morphisms.
To show: [math]F[/math] is an embedding if and only if [math]F[/math] is faithful and injective on objects.
First suppose that [math]F[/math] is an embedding, it is clear that [math]F[/math] is faithful.
Now suppose [math]FA = FB[/math], then [math]hom(FA,FA) = hom(FB,FB)[/math] and we have both [math]id_A \mapsto id_{FA}[/math] and [math]id_B \mapsto id_{FA}[/math]. Since [math]F[/math] is injective on morphisms, it follows that [math]id_A = id_B[/math] and [math]A = B[/math].
Conversely suppose [math]F[/math] is faithful and injective on objects.
Let [math]f\in hom(A,B),\; g\in hom(C,D)[/math], with [math] Ff = Fg[/math]. Then [math]hom(FA, FB) = hom(FC, FD)[/math] and so [math]FA = FC[/math] and [math]FB = FD[/math]. Since [math]F[/math] is injective on obs, we have [math]A = C[/math] and [math]B = D[/math] and [math]hom(A,B) = hom(C,D)[/math]. Finally since [math]F[/math] is injective on the hom-set restriction [math]F:hom(A,B)\rightarrow hom(FA, FB)[/math], we have [math]f = g[/math] as required.

"The angle OCD is a right triangle. Therefore CD= squareroot(OD^2 - OD^2)."
What fact about right triangles justifies this statement?

>>15039831
>Then hom(FA,FB)=hom(FC,FD)
You can't do that without some sort of surjectivity hypothesis on morphisms for the functor.

Honestly your proof for the converse is weird from the outset. Just do a generic contradiction proof.

The first part is fine tho.

>>15039872
my justification is that since the hom-sets [math]hom(FA,FB)[/math] and [math]hom(FC,FD)[/math] are pairwise disjoint, if they share an element [math]Ff = Fg[/math], they must be equal. Is this fine?
>generic contradiction proof
i don't see an obvious way to come up with one

>>15039943
>Is this fine?
Yes.
>i don't see an obvious way to come up with one
Assume [math]F(A) = F(B)[/math] where [math]A \neq B[/math]. Then [math]F(id_{A}) = id_{F(A)} = id_{F(B)} = F(id_{B})[/math], which contradicts [math]F[/math]'s injectivity on morphisms.
The faithful part is trivial.

>>15039958
thanks anon

>>15039741
>>15039627
The supremum simply means the largest possible
amount. This is almost similar in meaning to
maximum, with some analytical differences.

So, the supremum of the absolute difference
between two terms is the largest possible
positive difference. By adjusting the sequence
so that the terms become closer, the supremum
becomes smaller but it doesn't change what the
supremum means.

How often does a new moon occur and is a new moon always not visible?

Suppose I'm playing a gacha with probability p of pulling an SSR. Now, suppose I want to find the number of rolls n such that the expected value (of number of SSRs I roll) is equal to m. How do I do that?

What is a function i can define for any two sets?

I am trying to prove that
[math]X^{Y} = Y^{X} \Leftrightarrow X = Y [/math]

I need to define a function from X to Y so i can say [math]Y^{X}[/math] is not empty. I was thinking of the constant function, like f(x) = a. But a has to exist in Y first so I don't know how to proceed. Is there another function that guarantees Y is not empty or something?

>>15040990
If [math]Y^x[/math] is empty, that means there aren't any functions from X to Y. Isn't that only possible if Y is empty? And if Y is empty, doesn't that also mean [math]X^Y[/math] is empty?

No idea if any of that is right, just what my intuition is telling me.

>>15040990
I am not sure you have to do that. But you can assume Y is not empty for your proof if you want, so it contains an element a that you can use for your function f(x) = a. The a can depend on the set in question.

>>15041005
That seems true to me, but then I think the statement does not hold, since if Y is empty but X is not empty, [math]X^Y = Y^X = \emptyset[/math] but [math]X \ne Y[/math], right ?

>>15041020
Can we define functions from the empty set to a non empty set? I think the definition of a function [math]f: Y -> X [/math] just requires that every element of Y is mapped to some element of X. If Y is empty and X is not, then the empty set satisfies the requirement of being a function from Y to X vacuously. So actually, [math]X^Y [/math] would not in fact be empty. It would be a set containing the empty set.

I think I'm getting confused now.

>>15041030
>>15041020
>>15041016
>>15041005
Ty for your help anons, i'm also working on a similar problem which seems related

[math] Y^{X} = \emptyset \Leftrightarrow Y = \emptyset \wedge X \neq \emptyset [\math]

>>15041034
[math] Y^{X} = \emptyset \Leftrightarrow Y = \emptyset \wedge X \neq \emptyset [/math]
sorry

>>15041030
Just to clarify my train of thought here, I was thinking of functions as sets of ordered pairs. Since Y is empty, then the empty set satisfies (vacuously) the requirement that for all y in Y, there exists x in X such that (y , x) is in the empty set. Thus, the empty set is a function from Y to X. This tells us [math]X^Y[/math] is not empty while [math]Y^X[/math] is empty.

Which means your original statement holds.

>>15041030
>>15041037

Also i think you can, the empty set is vacuously true that it is a function from the empty set to any set

[math]\emptyset:\emptyset \rightarrow Y, \forall Y [/math]

I think this could be useful but im still not sure how to use it

>>15041040
oh very smart anon thats interesting

>>15041045
Let Y be the empty set. Let X be non-empty. Let x be an element of X. Since we can't map x to anything in Y, then there are no functions from x to Y.

Not sure how to do the reverse implication. Probably some contradiction or contrapositive proof. Like, suppose [math]Y^X[/math] is empty. Assume either Y is not empty or X is empty.
If X is empty, then we use the fact that we can define the empty set as a function from X to Y, contradicting our assumption.*
Now, suppose Y is not empty, then we can map an element of X to Y (go back to * if X is empty). This contradicts our assumption again.

This if X cannot be empty and Y cannot be non-empty, then we have the reverse inclusion

>>15040990
If [math]X=Y[/math] then [math]X^Y=Y^X[/math] is trivially true.
Conversely, assume [math]X^Y=Y^X[/math]. [math]X^Y[/math] is not empty because >>15041040
, so now let [math]f[/math] be an element of [math]X^Y[/math] then [math]f[/math] is a function from [math]Y[/math] to [math]X[/math] but [math]f[/math] is also in [math]Y^X[/math] so [math]f[/math] is also a function from [math]X[/math] to [math]Y[/math], so we have [math]X=\operatorname{dom}f=Y[/math].

>>15041198
Last line should've been [math] X = \mathrm{dom} \: f = Y [/math], this is because a function can only have one (unique) domain.

>>15040990
But that's not even true, like X = 2 and Y = 4 for example.

>>15041226
I think you are worthless

Assume for all [math]n \in \mathbb{N}[/math], [math]T_n[/math] is countable and [math]T_{n+1} \subset T_n.[/math]
Is [math]\bigcap_{n \in \mathbb{N}}^{}T_n = \varnothing[/math] ? How do I prove / disprove this?

>>15041394
Let [math]T_n = \mathbb{Q} \setminus \left(\bigcup_{k=0}^n \{k\} \right)[/math] then
[eqn]\bigcap_{n \in \mathbb{N}} T_n = \mathbb{Q} \setminus \mathbb{N}[/eqn]

>>15040947
Binomial distribution.

>>15041432
Thanks. Is there any condition for [math]T_n[/math]to satisfy such that [math]\bigcap_{n \in \mathbb{N}}^{}T_n = \varnothing[/math] ?

Why is [math]\mathbb{C}[/math] a linear space with infinite dimensions over [math]\mathbb{R}[/math]? Isn't it basically equivalent to [math]\mathbb{R}^2[/math] with some more operations?

>>15041462
Yes, such minimal condition that can be thought of is
[math]\forall{n\in\mathbb{N}}\;\exists{x\in T_n}\;\forall{m\in\mathbb{N}\setminus\{n\}}\;\;x\notin T_m[/math]

>>15041462
Sorry I meant
[math]\forall{n\in\mathbb{N},\; x\in T_n}\;\exists{m\in\mathbb{N}}\;\;x\notin T_m[/math]

>>15041961
It's two dimensional over the reals. A possible basis would be {1,i}.

I literally do not get Lagrangian mechanics.

When you plot [math]x^y = y^x[/math] on a graph you get a straight line [math]y = x[/math], and a curve. How do I calculate the equation of the curve?

>>15042300
y= -W(-log(x) /x) /(-log(x) /x)

Ahhhhhh I just don't understand probability theory at all. I'm gonna fail. Help

>>15042328
Huh. I suppose the answer isn't as clear-cut as I expected, then. Where do they intersect?

>>15042291
You can take the principle of least action as an axiom and derive all of mechanics from it. I liked Landau's Mechanics, though it is a pretty heavy text.

>>15042525
If you don't understand it, don't try to understand it. Just stare at the equations in the book until you know them by heart.

First of all, probability is not the same as possibility. If something is possible, it might or might not happen. If something is probable, there is a fixed likelihood of it happening (but it might not necessarily ever take place at all).
The probability of an event is determined by all of the possible outcomes that could take place, and by the number of outcomes that are equal to the event picked.
For example, if I had a teddy bear and had 5 people whom I could give it to, Lisa Jones, Mary Williams, Andrea Smith, Olivia Jones, and Samantha Epson, there would be 5 different possible outcomes. There are two people named Jones on the list of names above, so out of the 5 possible outcomes, there would be 2 possible outcomes that would result in me giving a teddy bear to a person with the last name "Jones".
If I could give it to any person from those 5 people whose first name ends in an "a", then I could give it to Lisa, or Andrea, or Olivia, or Samantha (keep in mind this is an exclusive "or"), so there would be a probability of 4/5 of giving it to a person with a first name ending in an "a" if I were to give it to any one person at random.
If one of those 5 people could give the teddy bear to another person once they got it from me, then there would be a probability of 1/5 of any one person getting it from me, and there would be 4 other people whom they could give it to, so the probability of me giving it, say, to Mary, and Mary passing it onto Samantha would be 1/5*1/4 = 1/20, assuming the second event were dependent on the first.
If the second event were completely independent (that is to say, if we could take for granted that Mary should have certainly been the one to get the teddy bear), then the probability of Mary giving it to Samantha would be 1/4.
This ought to at least get you started.

>>15042658
at x=2 and y=2

>>15042835
I mean where the curve intersects with the line. I think the x and y values at the point of intersection should be greater than 2.

is there a nontrivial pair of numbers such that the arithmetic mean of these two numbers is equal to the geometric mean of the two numbers

>>15042843
bro literally 2^2 = 2^2
x=y=2 so it's a point on the y=x line, and x^y=y^x too, so it's a point on the curve

>>15042882
x,y real numbers
(x+y)^2 = 4xy iff x=y

>>15042882
AM ≥ GM; equality holds if and only if all the numbers are equal.

>>15042887
I'm looking for the point where x = y intersects with y= -W(-log(x) /x) /(-log(x) /x).

>>15034337
Good Morning /Sci/entists!

If you are writing a radix 10 number like this 12345.

Five is in the one place. Four in the ten place. Etc. How is this indexed? Does index start with zero or one?
Is five in the first(zeroth?) index or the last one?

I made a faster maid space counter. As a way to test edge cases, I made some code that takes a digits index and makes it its max value. It indexes in a way such that radix 10 number 12345 would be like this
Index 0 -> 5
Index 1 -> 4
Index 2 -> 3
Index 3 -> 2
Index 4 -> 1

and max(0) would change the number to 12349.

If there is an established order and convention about if Index starts at 0 or 1 and which side is zero, then I will modify my code to obey it.

If there is no existing convention, then I am going to use the above described one and call it Maid Index of the number.

Thank you /sci/entists for reading my post.

>>15042923
I really don't understand what you don't understand.

let x0, y0 be the coordinates of the intersection point P between the two curves.

P is on the line of equation y=x, therefore y0=x0.

P is also on the curve of equation y^x=x^y, therefore y0^x^0=x0^y0.
x0=2 and y0=2 fit the description.
If you disagree with any of this, write it explicitly and say why.

>>15042943
There is no convention, although most languages use 0 as the starting index.
https://en.wikipedia.org/wiki/Comparison_of_programming_languages_(array)#Array_dimensions

>>15042952
Thank you for telling me fren. I am going to keep the term Maid Index then. A demonstration of the functionality is attached. I made a 2x2 Maid Digit and flipped it from max (15) to min 0), back to max, then counted to show next digit is created so the next number (16) is printed and first one is back to zero.

>>15042948
Okay, this is what I mean. When I plot x^y =y^x, I get pic related (forgot that the x = y line has to start from 0, as x and y cannot be negative).

What I am looking for is the point of intersection between this x = y line and the y = y= -W(-log(x) /x) /(-log(x) /x) curve, which is clearly not at (2,2).

What's a good book to learn natural deduction with?

>>15042958
Attached is the same technique being used to count to whatever 2^(100)+1,000,000,000 is. The count is in a 20x5 Maid Space because 10x10 was too tall to print nicely.

If you know an application for really big numbers, please tell me. For now I am using it to make a communications device. Maid Space will be used to send information over the Maid Phone on the Maid Parade Emergency Maidposting System. After that a very large distributed Maid Mind Counter will be deployed to volunteers with Maid Phones (or anything that has Java 18) so we can count to the maid and get her out of the library.

Thank you /sci/entists for reading my post.

>>15042969
Oh, one thing I forgot. I can count to whatever 2^(10,000,000,000)-1 is on the Science Computer, but I can't print it. If I try to put the whole thing in a StringBuilder, I crash from out of memory error.

Okay? So I changed the printer to print by row. Now a radix 2^(10,000,000,000) digit is just a 100,000 character line that gets printed. StrongBuilder is cleared and reloaded with next line and printed.

This prints maybe half way and then java just inexplicably stops. No explanation is given and I have never seen it before.

>>15042958
>>15042969
>>15042979
This is a question thread, not a blog thread. Did you get banned again from your usual haunts?

>>15043040
As far as I know I am not currently banned from anywhere. I just like talking to /sci/entists and dra/g/on maids. I posted here because I had a question and also there is no /sci/ equivalent of /dpt/. I tried to make Daily Science Thread once so people can talk about their experiments, but got told post here instead. Also I'm not sure if anyone else is doing experiments here.

I put it in /dpt/ too.

>>>/g/90214160

It kind of goes both places? For /sci/ because it has new math and for /dpt/ because I will use it in engineering Maid Phone software.

I guess for more questions, anything about high efficiency array math would be nice? Putting data in an image? Counting to a computer program?

I don't know exaxtly because I don't know what the instructions I am getting mean exactly. I might be the worst Computer Scientist in the world, but I am at least a Computer Scientist and there aren't very many of those in the world so it is hard to find people to argue with or ask and I don't know other science sites to post on except /sci/ that will let me post without logging in to something or installing something or other problems I don't like. I decline to use Reddit or Discord for any purpose (including just viewing data posted there).

Thank you /sci/entists for reading my post.

>>15042685
Maybe, but I don't really get the Lagrangian function or "generalized momentum".

>>15034337
Statistics people. I have test score data of a few different exam questions from a couple dozen students. The goal is to find which test question was the "easiest" to a 0.01 significance. Apparently, a Tukey test is inconclusive. But there is a test that can be used to perform this analysis between each pair of questions and find significant differences between the questions based on this data. But he won't tell us what test that is. Any ideas?

>>15043067
Specifically, I don't get the generalized momentum equation in Lagrangian mechanics.

>>15043152
Why would the change in the Lagrangian's value by a change in the "generalized" velocity give the "generalized" momentum?

Does coffee make you sleepier when it wears off?

Can someone explain what is happening in this video frame?
I know about the rolling shutter effect and banding caused by the flickering of the lights.
But I would expect the image to be slanted. In this case the image have intercalating horizontal lines, as if the camera is capturing only the even horizontal lines and then the odd ones. Is this ccrrect? Tje sources that I read only talked about the up-down motion of the rolling shutter.

So, is ablity to learn new things(math, chemisty or literature) random, or depend from your effort? I just talk with one human, who learning hard ,but have less result than me. I always think that all depends on how hard you work, but is it true?

>>15043189
If (L / generalized velocity) is a vector it could make sense. But why is it the (partial) derivative of L over the partial derivative of generalized velocity?

>>15043299
https://physics.stackexchange.com/a/628713
Why can you do algebra on their derivatives? It would make sense if it wasn't their partial derivatives.

>>15034337
Hi all, so i'm trying to lean math, I have some knowledge about high school math but anything will help.

Let [math]V[/math] be a finite dimensional vector space and [math]f: V \to V[/math] a linear operator. Given [math]v \in V[/math], let [math]Z_f (v) = Span(v, fv, f^2 v, f^3 v ...)[/math] be the cyclic subspace generated by [math]v[/math] under [math]f[/math].

Is the intersection of any two cyclic subspaces cyclic? i.e. is it always the case that given [math]v_1, v_2[/math] there exists some [math]v[/math] such that [math]Z_f (v_1) \cap Z_f (w_2) = Z_f (v)[/math]? I could not come up with a counterexample but I'm not sure how to prove this either because there seems to be no canonical choice of such [math]v[/math].

About acidity in chemistry, I know pKa and delta G are related, but I forgot in which way.
Does higher delta G means lower pKa or is it the opposite?

>>15043312
https://ww2.odu.edu/~skuhn/PHYS621/Lecture_5.pdf
why?

>>15043488
just read Landau's Mechanics (or chapter 12 of R. Douglas Gregory's Classical Mechanics) if you want to really "get" what it's all about instead of just solving problems
it's relatively complicated to derive everything and there isn't a nice one line answer that will make everything fall into place
you can differentiate with respect to a differential because it's just a function on time like any other, but to get why the derivative of energy is momentum read a textbook

is it normal that I was getting real erections since 5 years old? I don't know anything about biology

>>15039640
Anyone?

>>15039640
You should have an idea about the distribution function of the data.

>>15041198
>>15041061
Ty anons.

How can i prove:
[math] P(B) \sim \{0,1\}^{B} [/math]
I know i need to define a function from the power set of B to the set of all functions from B to {0,1} but i dont know what to do since these aren't normal sets. One is a power set and the other is a set of functions.

I tried to look up the solution online and in pic related but i dont understand it.

Also they dont prove the function is injective and surjective, which I have to do.

Normally for me to prove A ~ B i just need to define a function from A to B and prove it is a bijection.

>>15037607
>In what way does it affect me as a frontend web dev?
Have you ever seen color gradients on web pages? Have you ever come across interactive buttons and animations on web pages? Those things rely on linear transforms and sequences of finite differences.

>>15043740
Yes, but a frontend dev does not need to know that. They'll just codemonkey it.

>>15043695
I don't really know the exact distribution, I can only guess based on the 5 percentiles I have. Also I know that generally most data will be close to the minimum and less and less frequent for higher values. So the 0, 25 and 50 percentile are usually close and the maximum can really be arbitrarily large. Kind of like prices of some kind of product, most options are as cheap as it gets and some hipster brand will charge 5 times the average.
But it might be totally different, it's real world data and can really be whatever.

>>15042943
Bignums (variable-sized integers) are invariably stored in little-endian order (least-significant "digit" first).

For mappings between two prime fields
e.g. F2 -> F2, F3 -> F3
Are only the zero mapping and identity mapping candidates for linear mappings?
I looked at F3 and every mapping except these two fails at being additive.
Am I missing some obvious detail? If its true what im thinking, why is that? If its not, what would be a counter example?

>>15043717
Well, going by your picture (which contains a typo in the definition of [math]g_B[/math]), the author implicitly defines the function [math]f:\mathcal{P}(A)\rightarrow\{0,1\}^{A}[/math] so that [math]f(B)=g_{B}[/math] for each [math]B \in \mathcal{P}(A)[/math] where [eqn]g_{B}(x)=\begin{cases} 0 & \text{if $x\in B$} \\ 1 & \text{if $x \in A \setminus B$} \end{cases}[/eqn]Now we need to prove that [math]f[/math] is a bijection

Proof that [math]f[/math] is injective:
Assume [math]X,Y \in \mathcal{P}(A)[/math] and [math]f(X)=f(Y)[/math]. then we have [math]g_X=f(X)=f(Y)=g_Y[/math], so if [math]z \in X[/math] then [math]g_Y(z)=g_X(z)=1[/math] so [math]z \in Y[/math], and similarly if [math]z \in Y[/math] then by the same reasoning we have [math]z \in X[/math] so [math]X=Y[/math] by the the Axiom of Extensionality.

Proof that [math]f[/math] is surjective:
Let [math]g \in \{0,1\}^{A}[/math] so [math]g[/math] is a function from [math]A[/math] to [math]\{0,1\}[/math], now consider the set [math]X = \{x \mid g(x) = 0\}[/math] (This is the inverse image of {0} under g if you understand what that means) then [math]X \subseteq A[/math], i.e. [math]X \in \mathcal{P}(A)[/math]. So we have [math]f(X)=g_X[/math], now you can check that [math]g=g_X[/math], and therefore we found an [math]X[/math] such that [math]f(X)=g[/math] so [math]f[/math] is surjective.


Note that this may be a bit too long and detailed because i'm bad at being concise, in practice you won't find many mathematicians who write a detailed step by step (formal) proof. So you should also try to practice being concise, this is something i'm still trying to learn myself.

>>15043717
Also just in case you haven't figured it out yet, the intuition behind the proof is that if [math]B[/math] is a subset of [math]A[/math] then we have a unique indicator function [math]g_B[/math] which tells us which elements of [math]A[/math] are inside that subset or not (this function gives 0 for the elements of [math]B[/math] and 1 otherwise)

>>15043813
>>15043836
bless you anon, i never heard of an indicator function before, and ty for giving a detailed explanation it helps a lot. this is similar to how i have to prove these kinds of questions step by step and not leaving anything out and i struggle a lot when steps are left out so i appreciate it

Why do resistance and immunity have inverted definitions in biology from the rest of English?

>>15043893
They don't.

>>15043813
>now you can check that g=gX
anon im confused how do you prove that g=gX?

How do i prove
[math](X \times Y)^{Z} \sim X^{Z} \times Y^{Z} [/math]?

I have no idea how to construct a function between the two sets let alone prove it is bijective.

>>15044404
Use the projections [math]\pi_1:X \times Y \to X[/math] and [math]\pi_2:X \times Y \to Y[/math].
[eqn]\pi_1(x,y) = x \\
\pi_2(x,y) = y[/eqn]

With them you can just map
[eqn]f \mapsto (\pi_1 \circ f, \pi_2 \circ f)[/eqn]

What's the point of the Hamiltonian?

>>15044451
thank you anon, how did you think of this?

i am struggling so much with defining my own functions.

i was also trying to solve
[math]X^{Y\cup Z} \sim X^{Y} \times X^{Z} [/math]
and i thought maybe the function could be defined like
[math]f(x) = (x,\emptyset)[/math] if [math] \ x \in X^{Y} [/math] and [math]f(x) = (\emptyset,x)[/math] if [math] \ x \in X^{Z} [/math]

but i can't prove it is surjective because i need an (a,b) pair in the codomain and a or b must be the empty set.

>>15044520
you also haven't defined what happens in the case where x is isn't in either

Think about what objects are from the left hand side and a right hand side. An object on the left is a function from (Y union Z) to X. An object on the right is a pair of functions, one from Y to X and one from Z to X. Can you think of a way to turn one of these things into the other?

Y and Z need to be disjoint for your formula to be true btw

>>15044526
Can i define an identity function like
[math]
g:X^{Y} \rightarrow X^{Y\cup Z}
\\ h:X^{Z} \rightarrow X^{Y\cup Z}
\\ f(x) = (x \circ g,x \circ h) [/math]
?

I can't tell if what i'm defining is actually a legitimate function. I also can't tell if i'm supposed to always assume X Y and Z are never empty for these types of problems.

>>15044560
What type of object is (lower-case) x supposed to be here?

>>15044028
> antibiotic RESISTANT bacteria
> antibiotics do nothing to the bacteria
> use fire on something with FIRE RESISTANCE in video game
> It does less damage
> use fire on something IMMUNE to fire in video game
> it does ZERO damage
> system in human body that RESISTS disease
> "Let's call the IMMUNE system"

chemfags: i need some potassium glutamate (E622 food addditive) but no one sells it direct to consumers.
i can buy l-glutamic acid, and potassium bicarbonate. what ratio would i mix those in water to get monopotassium glutamate + co2?

>>15044644
i was hoping x would be a function inside X^YUZ, and then the complement functions x o g and x o h would point (a,b) back at x but i guess that doesnt work cause now two functions are pointing back at x.

im struggling to understand the intuition for how it is even true. if a function only has one unique domain and Y and Z are disjoint, then how can a function map one set to two separate sets? one of the elements of the pair has to be the empty set doesnt it?

like if the function inside X^YUZ is one that maps to X^Y, then it cant also map to X^Z, so then if (a,b) is in X^Y x X^Z, a or b has to be empty doesnt it?

>>15044134
To prove that any two functions are equal you need to show that they have the same domain and that they have the same values over that domain.

(i) The domain of [math]g[/math] is [math]A[/math] and the domain of [math]g_X[/math] is also [math]A[/math] so these functions indeed have the same domain

(ii) now let [math]z \in A[/math], if [math]z \in X[/math] then [math]g(z)=0=g_X(z)[/math], and if [math]z \notin X[/math] then [math]g(z)=1=g_X(z)[/math], therefore [math]g(z)=g_X(z)[/math] for all [math]z \in A[/math] so these functions indeed have the same values over their domain.

From (i) and (ii) we have [math]g = g_X[/math].

>>15043813
Just noticed that i made a typo in the proof that f injective, the 1 there should be replaced with a 0, becaus if z is in X then gX(z)=0

Need halp with problem. I guess it wants me to show that for each n, [math]A_n[/math] is countable and then show the countable union of [math]A_n[/math] equals A. The thing is, I just don't see how [math]A_n[/math] can be countable given the constraint of [math]A[/math]. Any idea how to approach this?

does this shit actually work

>>15044647
> resistance =/= resistant
> immunity =/= immune
ESL?

>>15044967
Nigga if pikachu is resistant to electric type moves it takes half damage and Sandshrew takes no damage from electric type moves because it has an immunity

>>15044647
the bacteria aren't immune to antibiotics, only specific ones. hence they have resistance but not immunity to that class of medicine.

immune is an adjective and also means protection, so it's just another way of saying the body's "protection system" against disease.

>>15044647
the bacteria aren't immune to antibiotics, only specific ones. hence they have resistance but not immunity to that class of medicine.

immune is an adjective and also means protected, so it's just another way of saying the body's "protection system" against disease.

How much statistics do I need to know to tell whether publications are trash or not? How do I learn it?

>>15043801
>Are only the zero mapping and identity mapping candidates for linear mappings?
Nah. Stuff like [math]x \to ax[/math] is also linear.
>>15044925
If the sum is always bounded above, then the [math]A_n[/math] aren't just countable, they're finite (there's a simple, explicit upper bound on [math]|A_n|[/math] which I'll let you calculate).
You then prove that, since all of the [math]A_n[/math] are finite, [math]A[/math] is countable.

Question, how well does Area under the curve (AUC) work as a metric for measuring effectiveness of a non binary(more than 2 options/classes) classification model (especially in keras)

>>15045325
Working forward, for [math]a_k \in A_n,[/math]
[eqn] \frac{m}{n} \leq a_1 + a_2 + ... + a_m \leq b[/eqn]
Then [math]m \leq bn. [/math] Is this related to the upper bound of [math]|A_n|[/math]? I have absolutely no idea where to go after this.

Electrical engineers, please help me understand this:

I was setting out to debunk the new-age theory of "earthing", which says among other things that our bodies need to be electrically nutralized by spending lots of time connected with the earth, since modern life has our bodies accumulating all this negative/positive charge (I've heard different things).

I assume that this is flawed theory, because as soon as you touch a grounded iron rod etc, you'll instantly electrically neutralize. I.e. humans are pretty much electrically in balance (neutral) most of the time, since we touch grounded metal stuff all the time.

However, I need help with understanding a video on the topic I found. This new-age guy on youtube is using a voltmeter that has one lead connected to ground, and one to himself. When he stands on some wood, the voltmeter reads 1.4 volts. When he steps down to the ground it reads 0 volt. When he steps back up, it reads 1.4 again. Watch it in 4k to see the details of the voltmeter.

Why does it read 1.4 V? What does that indicate? Would it read 0 if he had "spent more time grounding/earthing" as they claim?


https://youtu.be/V2814itbjaw?t=163 (2:43)

If I got a series [math](\{ a_n \}, \{ s_n\})[/math], related by [math]s_n=\sum_{k=1}^n a_k[/math], and the sequence of its terms converges ([math]\exists \lim_{n\to\infty} a_n[/math]), does it follow from that that the sequence of its sums [math]\{ s_n\}[/math] is monotonous?

Question about plasmon dispersion relation. Why does the attached plot implies that:
"for [math]\omega<\omega_p[/math] the propagation of transverse electromagnetic waves is forbidden inside the metal plasma. For [math]\omega>\omega_p[/math] however, the plasma supports transverse waves propagating"
?
I understand that the straight line is the dispersion relation of light in a dielectric and that the hyperbola branch is the dispersion relation of volume plasmons, but I don't get their interplay.

>>15043312
>>15043488
Just think of T as a function of q, so that T(q)=m*q**2/2. Then dT/d(x dot) is just shorthand for dT/dq (x dot) I would imagine.

I'm going through Lang's Basic Mathematics and got stuck on one of the problems regarding Isometry mappings.
The problem is in Chapter 6.4 - Multiplication Tables.
He proves that isometries for vertical and horizontal reflections are commutative but it is not proven for rotations and reflections.
He gives the solution HG^3 for row 2, column 5 in the picture, but from my understanding H o G doesn't equal HG^3.
The entire multiplication table idea seems fuzzy if you read the chapter.
Is this one of the errors people mention with regards to this book? I couldn't find anything about this chapter, only a youtube video where the author skips this section entirely.

I might not be able to respond immediately but I appreciate any input.

>>15045460
Sorry, I meant G o H doesn't equal HG^3.
In his definition for the table he states:
Where a row intersects a column, we have the value of the product of an element on the far left in the row, multiplied by the element on the top of each column.
So I'm assuming he means G o H in this instance, but he doesn't give any examples with the table in the exercise.

>>15043109
>I have test scores from students
>he won't tell us what it is
Are you a student?
In any case, why don't you just do paired t-tests for all question pairs, and use that to compare whatever you want to find?
I imagine you will not achieve a confidence of 99.9%, but you can try.

>>15045381
>If I got a series
Is [math] a_n [/math] a series or a sequence? If you meant sequence, then [math] s_n[/math] is called the partial sums of the series [math] \sum_{n \in \mathbb N} a_n [/math], and it converges only if [math] \lim a_n = 0[/math]. If all the terms of the sequence is of the same sign, then the partial sums are monotonic, otherwise they are not. Alternating geometric series is an example of a non-monotonic but convergent series.

>>15045373
Yeah.
Trivially [math]|A_n| \leq m[/math]

>>15045470
>student does a student's t-test
Pottery.

>>15045477
HOW

>>15039640
>>15043767
You _really_ should make an informed guess as to the distribution. Because you say it is financial data and has more values closer to 0, I would try to fit a lognormal distribution. You can easily do so in R, say, and then calculate your quantile.
If you don't want to use any kind of 'outside information', the best you can do is just linear interpolation.

am dumb
how to solve:
17^17^17^17 (mod 19)

>>15044505
it's the thing you derive the equations of motion from in QM
in classical physics it's kind of a meme afaik

>>15045504
note that by euler, for a != 0 mod m, a^phi(m) = 1 mod m. when m is a prime, phi(m) = m-1. therefore, a^17 mod 19 = a^-1. so 17^17^17^17 is nothing more than 17^-1. the inverse element of 17 is 9. so 9 is the answer.

>>15043528
What's a textbook with a good author like this but for quantum mechanics?

>>15045488
>>15044925
>>15044925
WLOG assume [math]b[/math] is an integer. If [math]|A_n| > bn[/math] then you may pick [math]a_1 \dots a_{bn + 1} \in A_n[/math] for which [math]b \ge \sum_{i=1}^{bn + 1} a_i \ge \frac{bn+1}{n} > b[/math], which is impossible. Hence [math]|A_n| \le bn[/math] for all [math]n[/math].

Now what can be said of the union [math]\bigcup_{n =1}^{\infty} A_n[/math]? Give an upper bound on its cardinality + determine how it relates to the set [math]A[/math], and you're done.

>>15044451
i am trying to prove this is injective but i'm stuck because i cant tell if g and h are injective, or even if this matters.

i have for f(x) = f(y)
xog = yog & xoh = yoh
am i allowed to remove g (like subtracting it from both sides) and do
x=y

or do i have to get rid of g by complementing xog with its inverse (which i dont know if it has), where gog^-1 is the identity function?

>>15044824
tyvm anon i forgot about that theorem i never knew how to use it

>>15043573
anyone?

>>15045476
Thank you very much. [math]\{ a_n \}[/math] is a sequence, but the pair [math](\{ a_n\} , \{ s_n \})[/math] refers to the series. I mentioned the relation between those two members to clear up confusion as then the limit of the series can be defined as [math]\lim_{n\to\infty} s_n = \sum_{n=1}^\infty a_n[/math] and I specifically wanted [math]\lim_{n\to\infty} a_n[/math] to refer to the limit of the sequence of the series's terms.

are there fourier transform equivalents which uses square, triangle, etc waves instead of sines?

>>15045493
Alright, linear it is then.
Thanks.

>>15044526
i thik i figured it out anon, can i do this?
[math]f:X^{Y\cup Z} \rightarrow X^{Y} \times X^{Z}
\\ g:Y \rightarrow Y \cup Z, \ g(x) = x \\ h:Z \rightarrow Y \cup Z, \ h(x) = x
\\f(x) = (g \circ x, \ h \circ x)
[/math]

this would be the path for gox: [math]Y \rightarrow Y \cup Z \rightarrow X [/math]

>>15043359
I'm still stuck and would love help if anyone has any idea :(

>>15045888
yeah, you just use replace the sin function in the equations with a square wave or whatever. not all (families of) functions work, but integer multiples of waves generally do.

Ok, so this one has been bugging me since Introduction to Chemistry years ago.

>Isolated room at 1 atm / 25 degrees Celsius and 0 % relative humidity
>Droplets of water at floor also at precisely 25 degrees Celsius
>No temperature difference between surroundings and the droplets
>Thus no heat transfer
>Yet the droplets vaporize

Where does this energy to change phase come from?

>>15046425
well, the water is at 25 C, so some molecules will randomly get enough energy to break from the liquid. another way to think of it is that the energy comes from the concentration gradient between the air (no water) and the water (lots of water), so the entropy of the room goes up even if the temperature drops.

How does General Relativity work?

>>15046425
From the water and the surounding air.
There's a reason why you can use the evaporation of water to cool things ...

>>15046620
>what is sweating

>>15046620
>>15046763
whoops, can't read, sorry

>>15046168
Tbh it’s interesting, but I’m too shit at math to solve it. I suspect the same for most others on this site.

>>15044404
Think in terms of the category theoretic meaning of the product.

A map from Z to XxY, is the same as an ordered pair of a map from Z to X, and a map from Z to Y. This is via the projections from XxY to each component.

>>15046569
It says how space and time are changed by the presence of mass. And it says how mass moves in space and time.

>>15046870
what's the main function used in general relativity? as in mathematical function

>>15046878
There are two: Tensors and Differential Geometry.

So I have a calculus paper to do about conservative vector fields and my teacher emphasized that he wants me to explain WHAT a conservative field is in the first place.
Like, what does it conserve? What in the real world looks like that? Why is it called that?
I tried looking it up but it's surprisingly hard to find a definitive answer. Most results are just about the calculus part.

>>15047073
a conservative field is a field such that path integrals only depend on their start and end points, i.e.
[math] \displaystyle
\int_{a}^{b} \vec{F} \cdot \vec{dl} = g(b) - g(a)
[/math]
where [math]g[/math] is just some other scalar function. this implies that closed loop integrals are zero:
[math] \displaystyle
\oint \vec{F} \cdot \vec{dl} = 0
[/math]
>What in the real world looks like that?
a gravitational field is conservative. work is [math]W=Fd[/math], so the change in potential energy as an object moves through a gravity field looks like
[math] \displaystyle
\Delta U_g = \int_{a}^{b} \vec{F_g} \cdot \vec{dl}
[/math]
since the field is conservative, we know that we can write [math] \Delta U_g [/math] as a function of just the start and end points, and in a mostly uniform field we of course can write
[math] \displaystyle
\Delta U_g = \int_{a}^{b} \vec{F_g} \cdot \vec{dl} = mgh_b - mgh_a
[/math]
where [math]h_a[/math] and [math]h_b[/math] are the heights of the two points.
a field is conservative if and only if its curl is zero everywhere. proving this is probably a bitch, but getting an intuition for it is easy if you think of force fields. if there was a place in space where gravity curled in a spiral, you could move an object in a path around that spiral and it would end up in the same place but presumably going a lot faster, and you could do this forever and violate the conservation of energy.

>>15047103
So it conserves evergy, right...?
Because it has no curl?

>>15047110
>So it conserves evergy [sic], right...?
if the integral is calculating energy, yeah it conserves it. i imagine this is the reason theyre called conservative fields, but im a bit rusty on my 19th century mathematics and physics history.

>>15047110
but also, just because a field isnt conservative doesnt mean it violates conservation of energy. electric fields, for example, are almost never conservative, but they conserve energy in conjunction with the magnetic field.

>>15047116
Thank you, truly.

>>15047119
anytime, fren <3

>>15045809
>you may pick [math]a_1 \dots a_{bn + 1} \in A_n[/math]
Okay so you can choose [math]bn+1[/math] element of [math]A_n[/math] as [math]|A_n| > bn [/math].
>for which [math]b \ge \sum_{i=1}^{bn + 1} a_i[/math]
Is this assuming [math]m = bn+1[/math]? What about the case when [math]m \not =bn+1[/math]?
I understand the rest of the argument but that part still bothers me.

>>15045749
>you may pick [math]a_1 \dots a_{bn + 1} \in A_n[/math]
Okay so you can choose [math]bn+1[/math] element of [math]A_n[/math] as [math]|A_n| > bn [/math].
>for which [math]b \ge \sum_{i=1}^{bn + 1} a_i[/math]
Is this assuming [math]m = bn+1[/math]? What about the case when [math]m \not =bn+1[/math]?
I understand the rest of the argument but that part still bothers me.

If i have a function f:A->B and B is a subset of C, how do i rigorously say f:A->C?
i was thinking ran(f) is a subset of B, B is a subset of C, so ran(f) is a subset of C.

now i'm not sure, maybe i can say f is a subset of AxC (since ran(f) is a subset of C), and then use that to say f:A->C?

>>15047265
>i was thinking ran(f) is a subset of B, B is a subset of C, so ran(f) is a subset of C.
This is fine.

What equation could i use to convert a heading times a movement into a position on a 2d coordinate system?
For example: say we're on a heading of 090 and advance 1 step, so we go from coordinates 0,0 to 0,1. if we turn to 180 and advance, now we're at -1,1. that's all easy, but say i want full 360 degree movement. starting from 0,0 and turning 123 degrees, how do i calculate where i'll wind up if i advance one step?

(This is really a programming question, but i'm looking for a mathematical answer rather than "oh, just use a function", unless the calculations involved are far more complicated than they would seem.)

>>15047336
if you start at [math](0,0)[/math] and turn at an angle [math]\alpha[/math], (measured counterclockwise), you will end up at [math](\cos\alpha,\sin\alpha)[/math].

>>15043359
>>15046168
>>15046765
Ditto, I suck at algebra. Still, I'm pretty sure the claim is correct.
Consider a digraph [math]G[/math] with at most [math]dim(V)[/math] vtxs. In particular, for your two fixed vectors [math]v_1,v_2[/math], label the vtxs [math]T^\ell v_1[/math] for [math]\ell\geq0[/math], similar for [math]v_2[/math]. These labels may overlap on some vtxs. Now, define there to be an edge from [math]T^\ell v_1[/math] to [math]T^{\ell+1}v_1[/math] if [math]dim(span(T^0 v_1,\dots,T^{\ell+1} v_1)) > dim(span(T^0 v_1,\dots,T^{\ell} v_1))[/math].
Since if [math]T^{\ell+1} v_1\in span(T^0 v_1,\dots,T^{\ell} v_1)[/math] then also [math]T^{\ell+k} v_1\in span(T^0 v_1,\dots,T^{\ell} v_1)[/math] for [math]k \geq 1[/math], and there are at most [math]dim(V)[/math] vtxs, you know there is at least one 'terminal vertex' in this digraph (a vertex you cannot leave).
After doing this for [math]v_1[/math] and [math]v_2[/math], you have chain(s) in [math]G[/math]. If these are non-overlapping, your intersection is [math]\{0\}[/math]. If they _do_ intersect, they must do so in some maximal vtx [math]x[/math], where maximality should be taken wrt chain length starting in [math]x[/math] and stopping in _the_ terminal vtx. Then the label of [math]x[/math] is the vector you seek.
Very sloppy sketch using probably not what you wanted, but if all you have is a hammer...

>>15047336
Polar to Cartesian (rectangular) coordinate conversion.

x = r sin(θ), y=r cos(θ)

where r is the distance and θ is the heading (measured clockwise from the y axis). Remember that sin/cos will expect arguments in radians.

How do I simplify 8^900 mod 29 using fermat's little theorem

>>15047657
[math]8^{900} mod 29=8^{29^2}\cdot8^{58}\cdot8 mod 29=8^4 mod 29=7[/math]

>>15047174
Nevermind, I'm fucking retarded. Just came home and read the hypothesis again. It makes perfect sense now.
tyvm 2hu anon and >>15045749

>>15045741
Original poster who named Landau and Gregory here
IMO it's super subjective to name the best book unless you're a master in the field, the first one you read you had no idea of the field, and then the second one is easier because you already had exposure from the first one and so on, you can't evaluate every book from a newcomer's perspective
Like for example I learned Lagrangian mechanics from Gregory (after skimming Susskind before and being totally confused), knew how to do exercises but didn't "get" it, then read Landau (which is a harder book with worse examples, but more abstract which can be good) and everything clicked
That being said the QM books I am familiar with are
>Sakurai (math heavy, boring but comprehensive)
>Bransden & Joachain (pretty terrible, spends too much time on boring topics like the hydrogen atom and scattering, my intro QM class used this)
>Susskind (le intuitive primer, people praise this to hell, idk what the big deal is) He also has a classical mechanics book named "The Theoretical Minimum" with a similar style. Lacks good examples imo
>Feynman lectures (less detailed but good side text, he really makes you think about experiments instead of axioms)
>Quantum Mechanics and Experience by Albert, comfy book with very simple conceptual explanations and then does a deep dive into interpretation and philosophy, lots of interesting stuff about heterodox views like Bohm, objective collapse etc
>Nielsen and Chuang, for CS fags who hate calculus (but maybe that's good because calculus being hard can distract from the important stuff), Nielsen also has a meme e-textbook called quantum.country (but that's just a few basic ideas aimed at non-physicists)
>Aaronson (almost all CS theory, filtered me hard)
there are probably like 10 more, people shill Griffiths (most upboats on SE fwiw) and Landau but idk about those (Griffiths electromagnetism is great though)
my advisor shilled me Cohen-Tannoudji but that's just him being a boomer ig

If I ask for hw help here will it take two days to get a response?

>>15048712
depends

>>15034337
Say a jump from 10m height is considered survivable. I need to find the area of a parachute A, such that you could survive a jump.

Do you guys have any idea on how to tackle this, it should be fairly simple, but isn't registering with me currently (drage force exercise).

>>15048977
Also, mass m = 50kg, of the guy jumping.

>>15048805
Is this the correct piecewise function for the above problem?


f(x) 40 {0 <= x <= 5}
70 {8<= x <= 18}
10x {5<= x <= 8}
70 {18<= x <= 20}

>>15048977
You need to know the drag coefficient for a parachute. A round parachute; a "square" parachute is essentially an inflatable wing, and the landing speed depends on the overall design and how well you time the landing (if you get it just right, the landing speed is zero).

Drag equation:
F=(1/2)ρ·v^2·Cd·A => A=2F/(ρ·v^2·Cd)
where ρ is the density of the fluid (~1.2 kg/m^3 for air at 20°C, colder air has higher density), v is the speed, A is the cross-sectional area, Cd is the drag coefficient (which depends upon shape).
Speed is presumably based upon the "10m jump" (which is rather high; you'll probably live ... if you get prompt medical attention). v=√2as, with a=9.81 m/s^2, s=10 m => v=14 m/s ≈ 50 km/h or 31 mph.
Force is 50 kg × 9.81 m/s^2 = 490.5 N.
=> A=2×490.5/(1.2×14^2×Cd) = 4.17/Cd m^2.

>>15049166
The non-constant parts are both wrong.
Solve for the linear function that goes through two points properly.

>>15049281
Thank you anon, God bless. Makes sense.

What are some ways of deriving a contradiction in an equality between two numbers (or sets) that you know are not equal?

like if you have x = y, but you know x is even and y is odd, you can do 2k = 2l+1 and show 1 = 2(k-l) so it implies 1 is even.

anything else like that?

Are there any good books to learn multivariable Calculus? I tried going through a chapter in Stewart's Calculus book but started getting annoyed by the repetitive exercises that appear unchanged every few pages and links to online videos.

>>15049696
If you don't have the patience to go through Stewart, you sure as hell won't have the patience to go through real Calculus books.

>>15049696
Apostol, Calculus or
Stephen Abbott, Understanding Analysis.

Has anyone ever checked behind the sun just to make sure there's nothing weird there? Just point a telescope and make sure there's no anti-Earth we can't see because it has a matching orbital speed

>>15049933
makes no sense

>>15049945
I meant a space telescope. Or launch a probe in an opposite orbit to the earth.

For every non-empty subset [math]A\subseteq X[/math], [math]U=\{ \sigma \in S_X \vert \sigma (A)=A\}[/math] and [math]V=\{ \sigma\in S_X \vert \forall a\in A: \sigma(a) = a\}[/math] are subgroups of [math]S_X[/math]. Why aren't [math]V[/math] and [math]U[/math] equal? Why is [math]V\leq U[/math]?

Somebody tell me how I can find the solution for equation of displacement from the differential equation of simple harmonic oscillation. I really suck at integration so I can't get through that part.

Why does it have to be disjoint unions?

>>15034337
Good Middle of the Night /Sci/entists!

I am writing about Maid Space with my Writing Computer. While writing about it, I was trying to figure out how to correctly say a number has a certain radix in LaTeX.

While reading about radix, I found out there can be a negative radix and even a radix which is the Golden Ratio Number!

I have no idea how these ideas work and I find them terrifying. What kind of math studies radixes?

I never heard this topic seriously discussed in a math class. Only ever saw it in Computer Science books when they explain things like binary, octal, decimal and hexadecimal. The only time I heard it mentioned in a math class was some type of history of math class where Babylonians got made fun of for using radix 60.

What kind of math cares about playing with radixes?

Thank you /sci/entists for reading my post.

>>15050053
see
https://en.wikipedia.org/wiki/Non-standard_positional_numeral_systems
https://en.wikipedia.org/wiki/Positional_notation#Mathematics

>>15050047
It doesn't have to be per se, it just is.

Where and when is this useful?

>the maps [math]X\to Y[/math] with a prescribed value at [math]x[/math] are in bijection with the maps [math]X\setminus \{x\}\to Y[/math]
how?

>>15050015
Because there's a distinction between fixing a set and fixing all the elements in a set.
Consider for example the group of rotations on the plane. The only rotations that fix lines going through the origin are the 0 rotation and the 180 degrees rotation, but the only one that fixes the points on the line is the identity.
>Why is V≤U?
If a symmetry fixes all points in a set then it also needs to fix the whole set.

>>15049933
https://en.wikipedia.org/wiki/Counter-Earth
tl;dr: there's no need to look; the L3 point isn't stable, an object in L3 wouldn't be at a constant 180° because Earth's orbit is elliptical, its orbit would be perturbed by other planets, and any sizeable object at L3 would have a detectable effect upon the orbits of other planets.

>>15034337
Good Morning /Sci/entists.

I have devised a means of encoding text into a Maid Space and then I can draw the Maid Space as a PNG image. Then the image can be read to retrieve the text. I created this intending it to be dual use. First, I can share much larger computer programs with saner architecture this way. It would replace stuffing everything in one file and putting it on pastebin, with posting an image on 4chan which contains the code project and maybe some version control information. Second, this encoding will be used to look for the Maid Mind Computer Program by counting big numbers.

Is there a good way in LaTeX to let people save the images from the PDF at their original dimensions? Dimensions would need to be preserved to ensure the data is read properly. If you change the scale then both the dimensions of the space and the data within will become garbled and useless.

Ideally I could put an image in my PDF and someone clicks "save as" or something similar to save an original dimensions copy of the Maid Space so the code in it can be read.

I have access to everything in texlive-full.

Thank you /Sci/entists for reading my post.

>>15050308
questions about the programming language [math]\sf\LaTeX[/math] are neither math nor science-related.

>>15050315
[math]\rm\LaTeX[/math] Is a markup language, not a programming language and it's math-related because it's used extensively in math papers and other papers which contain math.

>>15050327
There's no field in science or math that studies it, so it's unrelated.

>>15050315
>questions about a typesetting program commonly used by scientists and mathematicians is not related to science or math
>>15050349
>scientists and mathematicians have never studied typesetting
>the anon claiming this is talking to a computer scientist who is trying to typeset a math paper

>>15050327
> not a programming language
Not true. It's a language designed to generate input for Tex. [math]\LaTeX[/math] is Turing Complete. It can be used for programming (and people have) though it's not exactly the best language to use (ever).

>>15050358
A question regarding the usage of a program is technology-related. We have a sister thread over at /g/ for a reason, and none of your autistic bad-faith argumentation regarding the demarcation line will change that.

>>15050308
I don't care if LaTeX is a programming language or not. I just want to know is it possible to have a LaTex document contain an image which can be saved from the document at the original size of the image?

>>15034337
i cannot integrate tan(sqrt(x)) and wolfram isnt helping

>>15050400
Only way I think that's possible is to use a \href to the original source of the image. Any other method the image is going to be scaled depending on the output format, especially if the image is too large to fit a page.

>>15050426
That's known for being an especially hard integral and there is no 'simple' answer. Just google the equation and you'll find 20min long YT vids going through all the steps.

>>15050400
have you tried https://tex.stackexchange.com/

>>15050457
I can only find a ton of videos for the integral of square root (tanx) which is not what I'm looking for

4chan question. Is it possible to hide threads posted by maid anon? I hate her blogs.

>>15050478
mb about the vids, I misread the titles. But my point still stands, it's non-trivial. You can u-sub for u^2=x and integrate by parts but you are still left with a hard integral that requires the polylog function (which I think is that Wolfram is doing)

>>15050517
sure, just filter by Comment and use your most hated keywords.

>>15050517
If you filter the word "maid" you'll never see a post by Terry 2 again.

>>15050308
LaTeX is a typesetting system, not a file format or image manipulation tool. It is designed to produce high-quality documents, not to store or manipulate data. I would recommend using a different tool for your purposes, such as a programming language or image editing software.

>>15050544
>Terry 2
That's insulting. Terry was intelligent.

Why don't I feel any force when I touch something, especially something large like a building?

>>15050827
1. a building is not a point mass
2. even if it were, I doubt there's any building heavy enough for you to feel the effects

>>15050827
Because gravity is a very, very weak force (G = 6.6743 × 10^{-11}). That's why the gravity produced by the entire mass of the earth can be counteracted by a tiny magnet.

Is modal logic actually used like that in probability or is the AI bullshitting me?

>>15050827
You do not feel any force when you touch something because the force of your touch is not strong enough to be detected by your sense of touch. Your sense of touch is sensitive to mechanical pressure, but it is not sensitive to small or gentle forces. This is why you do not feel any force when you touch something, even something large like a building.

In general, the force of your touch is determined by the amount of pressure that you apply to the object that you are touching. The more pressure you apply, the stronger the force of your touch will be. However, in most cases, the force of your touch is not strong enough to be detected by your sense of touch, which is why you do not feel any force when you touch something.

There are also other factors that can affect the force of your touch and your ability to detect it. For example, the sensitivity of your sense of touch can vary depending on factors such as your age, your health, and the temperature of your skin. Additionally, the type and texture of the object that you are touching can also affect your ability to detect the force of your touch.

>>15050869
I said touch because distance reduces to 0, it's nothing to do with sense of touch.

is it generally true that [math]\operatorname{card }\bigsqcup_{a\in A} a = \operatorname{card }(a)\cdot \operatorname{card }(A)[/math]

>>15051018
*assuming every element of [math]A[/math] is of the same size

>>15034482
it has less science fiction behind it. if you're in the field, though, it's still making some very exciting breakthroughs.

>>15034337
Got absolutely railed on picrel...

What should I have done from here? Set some function g(x) equal to the integrand, take logarithm of both sides, then integrate? Or write the function by some power series? I'm clueless, obviously.. If it was just a simple u-sub or trig-sub, I'm never gonna make it..

How many ways can the digits from 0 to 9 be written in a row so that the even digits go in ascending order and the odd ones in descending order?

>>15034337
Is Inn(D_22) Abelian?

Here D_22 is Dihedral group 22 and Inn is the inner automorphism group

Does there exist an x in S_11 such that x^3 = (123)(45)?

When you throw something, like say a baseball horizontally, does your hand slow down in the last moments before you let go of the ball?
Or do you let go of the ball at the cusp of your hand's speed?

>>15051287
at the cusp of your hand's speed.

>>15050307
Thanks for the reply anon

>>15034337
not sure if this is the place to ask but is there a definitive guide to managing your time for school, this semester really kicked my ass and i want to fix my mistakes

>>15050862
Assume AI is bullshitting you until proven otherwise,
just to be on the safe side.

how do people even write pubs? it's absolutely mind numbing to read most of them.

>>15051255
The question boils down to the number of distinct permutations of eeeeeooooo. Which is 10!/(5!)^2 = 252.

>>15051929
It seems modal probability logic is an actual thing https://plato.stanford.edu/entries/logic-probability/#ModaProbLogi
Still can't find that formula anywhere, though.

I'm trying to implement a neural network from scratch, and I'm getting confused on when the loss function gets used. Say you have a NN with 1 hidden layer, and the error function is mean squared error.
Do you use the error function during backward propagation, gradient descent or something else? Does the implementation of gradient descent, backward propagation change when you use different loss functions?

im so unbelievably fucking tired

>>15052747
Same

>>15052508
> Does the implementation of gradient descent, backward propagation change when you use different loss functions?
No. The loss function is what 'rates' the prediction vs the desired output. So the back-prop implementation doesn't change but the loss function used in the comparison step can be user-defined.

>>15034337
How do I chelate my brain with lead?

Is it possible to find a path starting at the white vertex that goes through all other vertices exactly once and then returns to the start?

>>15052909
Yeah, sure. Can you not find any?

Everytime I try, I'm left with one unvisited edge.

>>15052932
Oh you meant edges, not vertices. Then no, because there are two vtxs with odd degree.

>>15052934
Oh yeah. Thanks. That makes sense. I've got it mixed up and forgot that two odd degrees can only exist if the starting point is not the same as the ending point.

>>15052003
thanks

>>15034337
It is mathematically ok to omit 0s in a vector to make working with it simpler right? Say I write r = (x, 0, 0) = x, this is legal right?