/sci/ - Science & Math

In theory, what does the action of a graviton look like? Is it like photons, where passing from a higher energy state to a lower energy state coincides with the emission of a force carrier particle? That is, are objects theorized to shed their energy in the form of gravitons as their orbit around a massive body decays?

I was wondering how to do the following in a Pig script: assume I have a relation A as follows:
10
5
2
I would like a tuple wise transformation to get:
5
3
null
That is the difference between one tuple and the next tuple in the relation, however I have not found a function that allows me to iterate through a relation.

D.U.M.B, everyone's accusing me!

~UNANSWERED~

Math
>>11379600
>>11382301
>>11388716
>>11388754

Physics
>>11379671
>>11384005
>>11386103
>>11387471 (car is moving at steady speed. then you brake the wheels on one side. then there is a torque about the center of mass on car. then it spins.)

Chemistry
>>11379673
>>11383793

Engineering
>>11387145

/g/
>>11385708
>>11385920
>>11385990
>>11385995
>>11386014 (this poor baby)

Stupid
>>11378381
>>11380385 (GL~)
>>11380442
>>11380531
>>11383910
>>11384039
>>11384227 (oh my god you are a faggot)
>>11386612
>>11386751
>>11387595
>>11388542 (power electronics, probably)

>>11388946
A graviton is an excitation in the gravitational field. Similar to how the EM field is quantized by promoting 4-gauge [math]A[/math] satisfying the wave equation [math]\Delta A = 0[/math] to operator-valued distributions/generalized [math]L^2[/math] sections on a principal [math]U(1)[/math]-bundle over Minkowski space, the gravitational field is quantized by promoting the metric [math]g[/math] satisfying the Einstein field equations [math]R - \kappa g = c T[/math] to an operator-valued generalized symmetric bilinear form on a Riemannian manifold. Let [math]S[g][/math] denote the classical Riemann-Hilbert action, this promotion [math]g\mapsto \hat{g} = g + \hat{h}[/math] leads to quantum corrections [math]\sim \langle \hat{h}\rangle + \dots[/math] in the free energy [math]F =-\ln \int dg \exp(-S[g])[/math], which constitute vertices of graviton exchange that mediate gravitational interactions. Objects feel gravity [math]precisely[/math] because they exchange gravitons.
>>11379671
Because compact universes must necessarily have non-trivial mean curvature by the geometric characterization of Riemannian spaces. By classical GR the curvature contributes to observable gravitational phenomena which, so far, do [math]not[/math] at all suggest any curvature even throughout the entire observable universe.
>>11386103
The Casimir force is caused by expectations of the Casimirs of the field algebra. You can study its effect in a cavity or region [math]\Omega[/math] as long as you can consistently quantize (find a *-irrep of) and diagonalize [math]at ~least[/math] the Poisson subalgebra [math]\mathcal{B}\subset\mathcal{P}(\Omega)[/math] at most linear in the momenta [math]p[/math]. A strip geometry turned out to be the simplest, since we can use Fourier coefficients.

>>11388995
Does anything prevent an isolate particle from forming an elliptical orbit around a gravitational body?

>>11389028
Why would it? All quantum corrections do is to impart uncertainty and noise to the [math]exact[/math] position of the particle, the classical contribution (consistent with Einstein/Newton/Kepler) is still the most significant, especially at large scales.

>>11388817

Question for evolutionary biologists

When we look at the phylogenetic tree of any species, we always see the name of a species at the end of one of the branches and go "oh yes, this one had a common ancestor with this other one here" and then point to where the branch veered off implying speciation.

The thing is, do we ever know what this common ancestor was? We always say, "this and this diverged from a common ancestor 5 million years ago" but do we ever know what that common ancestor was?

Is it not valid to say that that new species, through evolutionary time, became this new current species? Or do we always just say it was some different "common ancestor" that led to the more derived species?

Take, for example, whale evolution. Should I infer that basilosaurus and modern whales share a common ancestor that is unknown? Or would I be correct in saying that Basilosaurus is a more ancestral species of modern whales and eventually, through evolutionary time, became modern whales?

Like is basilosaurus a "transition" or the "common ancestor"? Know what I mean?

>>11379600
https://en.wikipedia.org/wiki/Silverman%E2%80%93Toeplitz_theorem
>>11382301
For eight digits, we have (26+26+10)^8 possible combinations. There are (26+10)^8 combinations without a capital number, and (26+26)^8 combinations without a number. We then have 62^8-36^8-52^8, and then we add back in 26^8(the ones without a capital and a number) because we removed it twice.
>>11388974
The third math question isn't a question, the fourth one has already been answered.

>>11389468
I forgot about the begin with a letter part.
Ah, well.

>>11388817
imagine a black hole. play time backwards until every particle that ever entered it covered the largest area in the history of said particles. Is it possible that a species in that border could fail to create a cannon/rocket/whatever even if they used ALL the matter/energy available as efficiently as possible? Like matter that created an even horizon once it was in a black hole had already created a gravitational field that couldn't be escaped no matter how you rearranged it?

>>11388817
>(Warn me if the link breaks.)
Link broke.

>>11389265
I'm not an expert but can try to answer,

The point you refer to is called an internal node, which are more precisely hypothetical taxonomic unit. So no. We don't know what specie/common ancestor is there.
These threes are just to show the evolutionary relationship between species (sometimes higher taxa), if you look at my image I found, you can see the shared loci used to construct these trees.
Trees made with morphological traits explained here:
https://www.khanacademy.org/science/biology/her/tree-of-life/a/building-an-evolutionary-tree

Basilosaurus share a common ancestor with modern whales, that line is extinct so it never became modern whales.
https://en.wikipedia.org/wiki/Evolution_of_cetaceans#/media/File:Cladogram_of_Cetacea_within_Artiodactyla.png

>>11388995
>By classical GR the curvature contributes to observable gravitational phenomena which, so far, do not at all suggest any curvature even throughout the entire observable universe.
That's odd, how could an experimental result have 0 uncertainty?

>>11388817
I don't quite understand how the answer was obtained for this question. It appears to be a simply P = F/A question yet inputting the values in as 1400/d^2pi doesn't seem to net the desired outcome. I'm bemused as to what could be the issue with this.

>>11388817
Pls help with simple proof.
(Rudin chapter 2 problem 6)
Let [math]( \mathbb{X} , d)[/math] be a metric space, let [math]E \subseteq \mathbb{X}[/math] and let [math]E^'[/math] be the set of all limit points of [math]E[/math]. Prove that [math]E^'[/math] is closed.

>>11389532
Works for me.
Try https://libgen.is/ , maybe your browser is defaulting to http instead of https.
>>11389815
He didn't say it has 0 uncertainty.
>>11389840
What definition of closed is Rudin using, [math]C =C'[/math]?
If so, show that the limit of a sequence in [math]C'[/math] is also the limit of a sequence in [math]C[/math] by using the ole triangle inequality trick.

>>11388817
How the fuck do I find the convolution sums limit for this?
Problem 2.3 of Oppenheims discrete time signal processing.
>Directly computing the convolution sum, find the step response of the LTI system whoms impulse response is:
[eqn]h[n] = a^{-n}u[-n] \hspace{2mm},\hspace{2mm} 0 < a < 1[/eqn]

There are 2 options for a convolution sum:

> 1) [eqn]y[n] = \sum_{k \in \mathbb{Z}} a^{-(n-k)}u[-(n-k)]u[k][/math]

> 2) [eqn]y[n] = \sum_{k \in \mathbb{Z}} a^{-k}u[-k]u[n-k][/eqn]

Im struggling to find the sum limits for any option, [math]a^{-k}[/math] or [math]a^{-(n-k)}[/math] will have non zero values for any k, the problem is the step functions. Pls help

>>11388974
are power electronics, and power systems in demand?

>>11389862
>What definition of closed is rudin using.
A set that contains all of its limit points is closed.
A set is closed iff its complement is open.

>[math]C = C'[/math] ?
Not necessarily, that would only happen on the case were C is closed, I believe.

>Sequences
We havent gotten to sequences yet bro

>>11389840
proofs everywhere dawg https://math.stackexchange.com/questions/15766/proving-that-the-set-of-limit-points-of-a-set-is-closed

>>11389870
Power systems is the most anus subfield within EE.
Doing power systems is basically learning 7000 regulations and being attacked by complex numbers in some disgusting 20x20 matrix you constructed using 10000 assumptions.
Fortescue theorem my ass, ive yet to find a proof.

>>11389828
1) 1400 kilograms is not the weight the shaft needs to support
2) πd^2 is not the formula for the area of a circle
>>11389870
Yes, they always will be

>>11389874
>we haven't gotten to sequences yet
Rudin calls accumulation points limit points?
Weird.
Anyhow, the stackexchange solution seems correct (the one by Caiceido, the OP doesn't work because it makes sense for arbitrary topological spaces, but doesn't work for them).

>>11389887
No, never mind, the OP doesn't work, but that wasn't the issue, and I was mixing up stuff with sequential spaces.
The simplest correction is that we have a neighborhood U of x, this neighborhood contains some y in E', and since U is also a neighborhood of y it has some z in E.

>>11389897
*open neighborhood, to be specific.

>>11389879
>ive yet to find a proof
It's just sliding around and adding vectors in the complex plane, bro

Is it true that in a ring, if an element is not a zero divisor, then it's a unit, and vice versa?

>>11389917
Absolutely fucking no.
Consider [math]x[/math] in [math]\mathbb{Z}[x][/math]

>>11389917
In finite rings, it's true! Let a have no zero divisors and consider the function f(x)=ax. Then f is actually linear f(x+y)=f(x) +f(y) so since the kernel of f is trivial, f is injective, and since the ring is finite, injective implies surjective so for some y, f(y)=1.
So your intuition was not totally wrong, as >>11389918
anon would suggest :)

>>11389862
>He didn't say it has 0 uncertainty.
He said it doesn't suggest any curvature, which is wrong. It doesn't suggest any curvature greater than the bounds of experimental uncertainty. I would also have clarified that curvature below the sensitivity of our measurements is entirely possible and likely given that the curvature of a close-to-flat universe grows exponentially.

>>11389920
I knew there was something I had forgotten.

>>11389920
>>11389926
Oh, is the converse true though? I.e. if you are a zero divisor, then you are not a unit, and if you are a unit, then you cannot be a zero divisor, finite ring or no?

>>11389932
That one's true.
If ab=0, then b b^-1=1 implies a1=abb^-1=0b^-1=0.

>>11389913
Not a formal proof. Shouldnt be called a theorem.

>>11389924
Oh yeah, that's right.
You also forgot about how he didn't mention that there could be an evil demon manipulating the data to make the universe's curvature undetectable.

>>11389868
The two sums are exactly the same.

>>11389897
Hmm this makes sense to me, I need to set up a triangle inequality to formalize this right?
>>11389902
All neighborhoods are open

>>11390020
Yes, that's what Im saying. The 2 sums are obviously the same, the problem is setting up the damn sum limits.

>>11390150
>I need to set up a triangle inequality to formalize this right?
Depends. Do you have the result that an (open) neighborhood of a point is also a neighborhood of every point it contains?
If you do, you don't need it, and this >>11389897 is fully formal and complete.
Otherwise, you need to either prove that, or show that if U is a neighborhood of x, it contains some y in E', and also contains some open ball around y.
For this, you can consider that U contains some open ball B around x, pass from U to B, there's some y in E' and B, and there's an open ball B' entirely in B centered on y (proof by triangle inequality). and it contains some z which is thus in B and then in U, completing the proof.

>>11390274
>Do you have the result that an (open) neighborhood of a point is also a neighborhood of every point it contains?

Question, why do you specify that an open neighborhood, etc?
We proved that all neighborhoods in metric spaces are open.

And yes, we did prove that every neighborhood of a point is a neighborhood of every point it contains

How do I solve 2 b and c?
since NH3 isn't a metal, i couldn't do it with the beta value as i did in A

>>11388817
c[x] = floor[x] -floor[x/2] -floor[x/3] +floor[x/6]
Notice how there are alternating steps of two widths: a shorter one with a width of 2, and a wider one with a width of 4.

I would like to create a similar function d[x] with the same property of steps going up by 1, and with the shorter steps having the same width of 2. However, I would like the wider step to have a width of 6, instead of 4.

How do I achieve this?

>>11390524
Because we're used to different definitions.
In my experience, a neighborhood of x just has to contain some open set around x.
>>11390755
[math]floor( \frac{x}{8}) + floor ( \frac{x-6}{8})[/math]

>>11390825
>floor(x/8)+floor((x−6)/8)
Thanks! May I ask how you knew to do that, so I can generalize it if I ever need to do similar stuff? Or was it just trial and error?

>>11390825
>In my experience a neighborhood of x just has to contain some open space around x

Rudin defines a neighborhood on a metrix space [math]\mathbb{X}[/math] as follows:
>"A neighborhood [math]\mathcal{N}_r(x)[/math] is the set of all points [math]p \in \mathbb{X}[/math] that satisfy [math]d(x,p) < r[/math] with [math]r>0[/math]"

Isnt this equivalent to your definition?
Im genuinely asking, not trying to be annoying.

>>11390876
6+2=8.
So I decomposed into a sum of two functions, both going up by one with every eight steps, but one going up six steps after the other one.
>>11390884
That's closer to the definition of the open ball.
They aren't equivalent. For example, [math]\mathcal{N}_1 ((0, 0)) \cup \{ (2, 2) \} \subset \mathbb{R}^2[/math] is a neighborhood of [math](0, 0)[/math], but it's neither open nor is it a neighborhood of [math](2, 2)[/math].
Also, I used your N notation, but what you'll commonly see is [math]B_r(x)[/math], where the B stands for "ball".

>>11390899
Interesting. So that suggests an alternate way to write the function I had as:
c[x] = floor[(x+5)/6] +floor[(x+5-4)/6]

>>11390899
Yeah Rudin defines ball using the euclidian metric.

Namely:

>The euclidian metric for a metric space [math]\mathbb{X} = \mathbb{R}^k[/math] is [math] d(\boldsymbol{x} , \boldsymbol{y}) = || \boldsymbol{x} - \boldsymbol{y}||[/math] where ||a|| is the euclidian norm of a.

>An open ball with center [math]x[/math] in a metric space [math]\mathbb{X}[/math] is the set of all points [math]p \in \mathbb{X}[/math] such that [math]||x - p|| < r[/math] with [math]r > 0[/math]

Basically rudin restricts balls as a neighborhood specifically defined using an euclidian metric on an euclidian space.

Your concept seems better, as its more general.

why is the percent overshoot for the model response of my system larger than the actual response, and why is its rise time shorter? Do all dominant pole model systems do this?

>>11391005
wait I think I got it, is it because the less dominant poles only affect the transient response of my system so by using pole cancellation, my rise time is shortened and my overshoot is increased?

how are chickens/eggs impregnated if roosters don't have a dick?

>>11389879
>>11389885
that's disappointing to hear, I'm interested in communications and RF/Microwaves.

Why is lithium chloride toxic for consumption, but not sodium/potassium/rubidium chloride?

>>11391089
See pic related about bird reproduction.
I'm npt sure how much the process changes for chickens in specific.
Actually, I'm basically answering this to reduce the tally later.

I’ve been giving some thought as to how to make a truly natural unit of measurement. 1/299-something times the speed of light seems a bit random. What about a unit of length equal to the normal size of the human penis?

>>11391384
thank you

bros what did i do wrong?
there is still one more part left to this so i know that they're not asking for the answer but the step inbetween, but i keep on getting it wrong

>>11388817
I have to multiply two vector to get a new vector. Am given a vector D with the magnitude of 10.0 m and an angle of 143 and Vector A with a magnitude of 8.00 m and an angle of 270.
I solved for the i and j, but am missing k.

Ok so I apparently expanded it incorrectly?
Can someone tell me why (x^2-4) is expanded as (x-2)(x+2) instead of (x+2)(x-2)?
See pic attached for a visual representation of my

Is there a reason the speed of light is equal to c, or is it possible for the NWO or whoever to adjust it in the admin control panel of the universe?

>>11391488
>>11391462
Like I know that they're the same thing but why did the system only accept my answer when I did (x-2)(x+2) instead of (x+2)(x-2) when solving for the partial fractions, like does it even matter??? Sorry if I'm being fucking dumb but I seriously don't get why they didn't accept the first pic and forced me to do the second.

>>11391488
>>11391497
>does it even matter?
No, but computers do that sometimes.
Try ordering them next time so that the numerators are increasing, I think that might be the standard they're expecting.

I have a test tomorrow, and have a few questions.

>If I have a square root number thats negative, like -27, but I have a index of 3 (or odd number), is it still considered an imaginary number?

>if I have a fraction, and I only have the numerator or denominator with a negative number(-3/4), does the fraction stay negative? (like multiplying with a negative number)?

>this kind of same question is previous, If both numerator and denominator have a negative number does it go to positive? (-3/-4) -> (3/4)

>what method(s) do you have to understand, and label complex and other types of numbers? (real,imaginary,irrational,integer,non-integer,counting,real etc..)

>>11391488 (checked)
A, B, and C will not be the same if you do it the first or the second way. Both ways are fine, as addition is commutative. But if you're putting your answers into a computer (for, say, homework) and you write
[math]\frac{-2}{2x} + \frac{\frac{3}{8}}{x+2} + \frac{\frac{5}{8}}{x-2}[/math]
or you write
[math]\frac{-2}{2x} + \frac{\frac{5}{8}}{x-2} + \frac{\frac{3}{8}}{x+2}[/math]
then your decomposition is correct either way, but you need to be careful if they're asking you what [math]A, B, [\math] and [math]C[/math] are.

>>11391641
Yeah I think my error was solving for C first instead of B, which is probably why I got it wrong I'm thinking. I got what you mean by other half about addition though, thank you! >>11391524
Thank you too, I got the explanation!

>>11391557
holly shit i hope you dont pass fucking brainlet chink. this is elementary tier
>yes, of course. ANY sqrt of negative is imaginary by definition
>yes
>yes
>i=sqrt(-1) thats all you need to know

How to calculate the electric field due to a ring using gauss law ?

>>11391690
Thanks for the help, and you might be right on me being brainlet, this is the second time I am taking this class in college. If I don't pass this semester Im going to drop out of college. No point trying anymore.

Straight up, how do you people even sort your library of PDF files and research that you have scoured from the internet?
I have not, and I have a chaotic system right now, not even renaming the files.

What does script C() mean here? At first I thought it was span() but they go on to use span() later in the document so I'm not sure if it means something else or the notation just gets switched up.

>>11391723
It's alright bro, I'm taking a class for the third time and if I don't make it, I'll be switching majors or dropping out as well. Just don't give up, I know I damn well want to disappear but you need an anchor.

>>11391788
I coasted through school barely passing my grades. I wish I didn't though, but now Im trying to make up for it in college.

>>11391802
I know, that's my situation as well. I'm paying for my coasting three-fold, just know that there's always someone way more fucked than you are bro, don't give up because I haven't.

>>11391820
You called me a brainlet chink, I mean *shrugs* I pretty much am if I can't pass this class after doing it a second time, especially with it being elementary tier.

>>11391842
I'm not the person who called you that lol

>>11391859
>tfw this is a anon message board and anyone could be anyone.

My mistake.

I'm feeling awfully stupid to not get this question, but here goes.

If F[math]_n[/math] = 2[math]^{2^n} +1[/math] then show show that 2[math]^{F_n - 1}[/math] is congruent to 1 mod F[math]_n[/math].

Any help would be nice. I basically just have spent hours coming up with equivalences and rewriting them.

With regards to 14, what does it mean by "integral factor"?
Apparently the answer is D. I feel like I'm missing something simple.

>>11391694
Does it need to be with Gauss's Law? I don't think that's possible.
It'd be way easier to sum the fields due to each point along the ring.

>>11388974
is there a scientific reason as to why I find this gif sexually attractive?

>>11392214
I think it just means integers that factor into it, like 1, 2, ..., 1992.
In regards to getting the answer, I think it's a matter of seeing that two factors that multiply to an even integer like 1992 are either both even (e.g. 2 and 996) or one even and one odd (e.g. 3 and 664), so you get 3/4 even, although I'm not positive on that reasoning.

>>11392262
Humanoid body with feminine curves, swaying hips, and large pupils

Not a /sci/ lurker. Sorry if this isn't the appropriate thread.
The other day I read about there is a correlation between age of the parents and chance of known genetic defects, such as Down's Syndrome. The age of both parents is important. Pic related is an example.
I'm wondering if there's more to that. Not a scientist so I have trouble expressing my thoughts on it. Getting Down's is sort of yes/no, 1/0 digital question. You either have it or not. The same thing applies to other defects studied. What I'm wondering is: could it be that age not only increases the risk of those defects appearing, but also carries other defects that are more difficult to asses and are more in an analog range? For example, slight increase of getting cancer, slight decrease in fertility, slight decrease in intelligence, etc.
It makes sense to me since I think chromosomes degenerate over age. So passing your genes at 40 might be bad for your child even if he isn't born with a particular syndrome.
I guess this might be difficult to test in humans. But maybe it could be done with controled mice population? One population is bred over 100 generations at a very young age. The other is bred over 100 generations at a very old age. Both 100th populations are tested for several generic health indexes.

Maybe this has already been tested and is known, but I've tried to google it and had no luck. Maybe I'm not using the appropriate terms, or I should look into specific science search engines.

I'm a bit worried because my grandma had my mother at an old age, my mother had me at 39yo and I'm already 31 and still have no kids.

Thanks and sorry for the long post.

thoughts on my solution?

>>11392623
Every blue hexagon is made up of 6 triangles of the same size as the red triangles.
It you know that, it becomes visually obvious for every 6 blue triangles (an hexagon) you need 2 red ones, no matter what angle you tile them in.
Your solution is correct.

Prove that for n -> ∞
[math](\frac{n}{n+1})^{n^{2}+1} = 0[/math]
Use Bernoulli's inequality.

I dun get it. What is my r and my x (going by EN Wikipedia's notation) here? I can see something having to do with the n+1 in the fraction, but nothing else.

Where do I get articles when sci-hub fails me?

>>11392875
If you're enrolled at a university, you likely have access to academic papers thru your library. Have you tried that?

>>11392880
>If you're enrolled at a university
Hurr durr I'm not anymore or I wouldn't be asking.

>>11392884
>hurr durr
This is the [math] stupid [/math] questions thread after all. What paper do you need? I might be able to get it for you.

how can I manage a ven diagram with a lot of entries? 7 separate lists? is there a better way?

>teacher laughed loudly immediately after seeing my assignment
should i just end it?

>>11391486
>vectors have magnitude and one angle
Are you trying to multiply vectors in 2D space and expecting a 3D vector?
>>11391785
I have multiple folders named after prostitutes I had sexual relations with and ex-girlfriends.
I sort files according to which pain or which sorrow the .pdf file brings to my heart.
>>11391786
[math]\mathcal{C}[/math] for collumn space, most likely.
>>11392623
Slick.
>>11392867
Use [math] ( \frac{a}{b} )^n = \frac{a^n}{b^n}[/math]
>>11392884
>hurr durr
Duur hurr durr duur? Hur hurr dur duur huur durr.
>>11393503
>he doesn't add in jokes and banter to his assignments
>his professor doesn't reply with his own jokes and banter in the correction
What are you lads even doing?

I'd really appreciate an explanation here...

I get the following points

1) Mass and Energy are equivalent. A flash light loses mass when it is turned on, because some photos escape. And this relationship is captured by E = MC^2.

2) Gravity and acceleration are equivalent. If you're accelerating in space, or are on a planet with a large mass, you will experience the same thing.

3) The speed of light is constant, and faster-than-light travel is impossible.

Now how do you go from points 1 and 2 to point 3? I keep reading that faster-than-light travel is impossible because as you approach C your energy approaches infinity, but how do you derive this idea from the postulates above?

>>11393686
>Are you trying to multiply vectors in 2D space and expecting a 3D vector?
I think he is talking about the cross product. I'm not about to parse thru his question tho.
>>11393503
Do share what happened lol

>>11393503
Do share what happened lol
>>11393686
>Are you trying to multiply vectors in 2D space and expecting a 3D vector?
I think he's talking about the cross product. I'm not about to parse thru his question tho.
>>11393707
Point 3), speed of light being constant for all observers, is an experimental fact and also one of the postulates that you take for granted in special relativity. Then 1) follows when you develop special relativity. The equivalence principle, 3), is a separate idea.

>>11393723
The equivalence principle, 2), is a separate idea***

>>11393723
>>11393727
Thanks. Is it easy to understand how C is determined to be constant and how mass-energy equivalence follows?

>>11393856
C being constant is the postulate.

>>11393856
https://arxiv.org/ftp/physics/papers/0308/0308039.pdf

is the answer to this
2x(-x^2-1)cos^4(-x^2+1) ?
and how do I tell if it's increasing or decreasing at that point?

Is there an internet source people can recommend for learning beginner calculus? I've had such a spotty education my fundamentals are weak and my definitions confused. I've dropped a calculus course 3 times in my life, now I want to learn it not for school but because it bothers me that I don't really know what a derivative is and how it works. I need something clear and would be very grateful for assistance.

>>11394139
>2x(-x^2-1)cos^4(-x^2+1)
Yep. That's what I got. So what does that expression represent? It represents the slope of F(x). [eqn] \frac{\text{d}F}{\text{d}x}\Bigg|_{x=1/2}=2(1/2)\big(-(1/2)^2-1\big)\cos^4\big(-(1/2)^2+1\big)=(-5/4)\big(\cos(3/4)\big)^4 [/eqn]
which is definitely a negative number. So F(x) is decreasing at x=1/2.

>>11394139
>2x(-x^2-1)cos^4(-x^2+1)
Yep. That's what I got. So what does that expression represent? It represents the slope of F(x). [eqn] \frac{\text{d}F}{\text{d}x}\Bigg|_{x=1/2}=2(1/2)\big(-(1/2)^2-1\big)\cos^4\big(-(1/2)^2+1\big)=(-5/4)\big(\cos(3/4)\big)^4 [/eqn]
which is definitely a negative number. So F(x) is decreasing at x=1/2.
>>11394277
Khan Academy.

Could someone explain how this works to a brainlet?
Where did the [math](sr^i)(r^{n-i})[/math] even come from?
How would I come up with this on my own?

What matters more for getting a job (USA) after grad school: the general prestige of the university, or the university's ranking for just your specialization, or maybe just the lab(s) and professors that you research with? i have applied to a few universities and some are great, but arent huge names outside my field, while others are well known like princeton, columbia, etc but not as good in my specialization

>>11394277
khan academy or MIT OCW

Can you be shocked by a high enough voltage power line by grabbing a single phase? I figure you’re essentially a capacitor being quickly turned on and off so there must be some kind of current, not sure how to calculate it though.

>>11394277
A derivative of a function is just another function that describes the tangent slope of each point on the first function. An example: if you had a graph showing your position at time, the derivative would describe your velocity. You can calculate the derivative of a function with
[math]\lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/math]

There's a ton of videos on basic calculus like this, khan academy probably the most popular. Get derivin', champ!

What do math professors do their research grants? AFAIK they don't really see any of it other than in the summer. Is it just for summer funding?

So you supposedly can't understand certain particle interactions without knowing the math behind them, but what exactly does the math tell you that is so important? For example, when describing the evolution over time of a hydrogen atom in an otherwise empty universe where the most probable location of the proton is 1 light year away from the most probable location of the electron. Why does this scenario need mathematics to describe?

>>11395035
Your post pretty clearly demonstrates why mathematics is necessary to describe physics: because otherwise you make nonsensical statements and nobody understands what you're saying.
Here are some other good reasons:
1. Physics is a science. Not philosophy. You make predictions and construct experiments to validate (or otherwise) the theory that led to those predictions. You want quantitative agreement because statistical uncertainties are unavoidable and you can't do statistics on qualitative observations.
2. A mathematical theory puts strong, specific constraints on what it does and does not predict. Physicists are not typically rigorous in the sense of mathematicians, but it's better than nothing. Much better, I should emphasize. It makes very clear what can or cannot occur within the framework of the theory (assuming infinite intellectual power from the physicist).

How do I stop being lazy/procrastinating everything and get good at studying before August?

Absolute brainlet here, having brain problems.

I'm doing maximum revenue problems. I understand that the equation for a particular problem is that Revenue = 300x - x^2/20. I understand that if you were to graph this it would show the aggregate revenue at each increment of the product's price, I understand that the price goes down by .05 for each unit sold and that the profit PER UNIT sold goes down by .10 with each unit sold. I understand this because I graphed the data 1 by 1. What I don't understand is how you KNOW the maximum revenue is in fact the maximum short of graphing this. The vertex is at 3,000 units sold, but if the numbers in question were too large to graph (and arguably they are) how would you know where the maximum was? How could you be sure?

Could someone explain to me how aldolic and crotonic condesation work in the simplest possible terms? Or maybe give me some simple examples so I can understand what happens.

When I boil "spring water" in a clean vessel, a film appears over it. It looks oily/waxy, and faintly brown.
Pic related, skimmed the pot
Its ozonated water.

Bros, how do you quickly sketch level curves? I waste too much time when I'm studying. For example, f(x,y)=(x^2+y^2)log(x).

>>11391945
idk. This latex has some 2^stuff voodoo in it, maybe something useful 4u

[math]

\delta \, \epsilon \left ( 0,1 \right ) \\
\displaystyle
\prod_{k=0}^{n} \left ( 1 + \delta ^{2^{k}} \right )
= (1+ \delta)(1+ \delta ^{2})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}}) \\
(1- \delta) \prod_{k=0}^{n} \left ( 1+ \delta ^{2^{k}} \right )
= (1- \delta)(1+ \delta)(1+ \delta ^{2})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}}) \\
= (1- \delta ^{2})(1+ \delta ^{2})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}}) \\
= (1- \delta ^{4})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}})
= (1- \delta ^{2^{n}})(1+ \delta ^{2^{n}}) = 1- \delta ^{2^{n+1}} \\
\\
\boxed{(\delta ^{2^n})^2 = \delta ^{2 \cdot 2^n}=\delta^{2^{n+1}}}
\\
\displaystyle
\prod_{k=0}^{n} \left ( 1+ \delta ^{2^{k}} \right )
= \dfrac{1- \delta^{2^{n+1}}}{1- \delta} \\
\displaystyle
\lim_{n \to \infty} \prod_{k=0}^{n} \left (1+ \delta ^{2^{k}} \right )
= \lim_{n \to \infty} \dfrac{1- \delta^{2^{n+1}}}{1- \delta} = \dfrac{1}{1- \delta}
[/math]

>>11392262
freak
>>11394576
Yes. You can be shocked by a single phase at low voltage too. You can ever be shocked by DC. Have you really never been shocked before? Humans don't make great capacitors.
>>11395842
[math] R(x)=300x-x^2/20 [/math]. The maximum occurs when [math] R'(x)=300-x/10=0 [/math] so we get a maximum revenue at [math] x=3000~\text{units} [/math] of [math] 450,000~\text{dollarydoos}
[/math]. No graphing required. Just set the derivative of R(x) to zero. Elementary calculus, love.
>>11396159
If you're just studying, use this. https://www.geogebra.org/3d?lang=en Of course, you should know how to draw a level set.

>>11396222
>Just set the derivative of R(x) to zero.
Yes but why does this work is my question really, not every value yields the extremes of the function, why 0?

>>11396235
It is a fact/theorem that extrema can only exist at critical points (i.e., at places where the derivative is zero or at the boundaries of the interval the function is defined on). https://en.wikipedia.org/wiki/Fermat%27s_theorem_(stationary_points)

>>11396235
We have a differentiable function [math]f : X \rightarrow \mathbb{R}[/math].
As you well know, the derivative is the growth rate of the function. So if at some [math]x_0 \in X[/math] we have [math]f'(x_0)>0[/math], moving a little bit to the right would increase the value of [math]f[/math], and moving to the left would decrease the value of [math]f[/math]. If [math]f'(x_0)<0[/math], we have the opposite, and this all seems to imply that maxima and minima can only be reached in points with [math]f'(x_0)=0[/math].
Notice the "if we can move a little bit to both sides." This has a precise definition as [math]x_0[/math] being an interior point of [math]X[/math]. For example, [math]1 \in [0, 1][/math] is not an interior point, and [math]f(x)=x[/math] attains its maximum in it.

Hey guys, retard here.
I have a dynamics lab to write up and want to ask for some advice. We measured the number of oscillations of a trifilar pendulum for a certain time, in two stages, one with a mass added and one without, and calculated the moment of inertia of the mass. Now we have to do some error analysis. Two questions.

1) What extra methods could I use to do error analysis? The method that has been suggested is the standard deviation. I would like to use the suggested method, in addition to something else to get a better grade for my report. But it has to be realistic and something I can do in a week or two.

2) What software can I use to plot the normal distribution?

T-t-thanks.

>>11396555
>What extra methods could I use to do error analysis?
Use prorogation of error to get the total error on all calculations.
>What software can I use to plot the normal distribution
Excel

>>11396222
...... i like this gif too, it's very cute

I've lost my wallpaper.
Scientifically rate this one from 1 to 10 in the autism scale.

>>11396684
Also this one.

I'm taking computability & complexity theory next semester. What are the most relevant set-theoretic theorems that I should be aware of?

For example, it is known that if [math]\Sigma[/math] is some finite/countable alphabet, then [math]\Sigma ^ * = \bigcup_{n \in \mathbb N} \Sigma^n[/math] is countable, whereas [math]\mathcal P (\Sigma^*)[/math], [math]\Sigma^{\mathbb N}[/math] are of of size continuum. Any other useful "facts" such as these that I should consider?

If I'm standing on the roof a car with a constant velocity of 60 mph and I jump would I safely land on the roof of the car?

>>11395842
your function 300x - x^2/20 is a quadratic function: it contains x^2 and no higher powers of x. the graph of a quadratic function is a parabola, always. it's possible (and very easy) to compute the vertex of the parabola algebraically by a method called "completing the square".

if it happened that your function is something else than quadratic, then it's also possible to find extrema of the function, but you need to use derivatives.

>>11396698
This one too.
>>11396699
Countable union of countables is countable.
The grand trio of Choice, Well-Ordering and Zorn.
[math]X \times X[/math] has the same cardinality as [math]X[/math] if [math]X[/math] is infinite, see https://en.wikipedia.org/wiki/Tarski%27s_theorem_about_choice
Infinite sets are Dedekind infinite. See also the other characterizations here https://en.wikipedia.org/wiki/Dedekind-infinite_set

That's it, I think.

>>11396555
>>11396565
Any other suggestions? What about using partial derivatives?

>>11396758
Forgot this one: https://en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Bernstein_theorem

>>11396610
>
>>11396758
I like this one c:
>>11396714
You can't neglect air resistance in this situation. The drag force on the person would be [math] F_d=C_dA\rho v^2/2 [/math]. If the person normally can normally jump a height [math] h [/math] then they are airborne for [math]t=\sqrt{2h/g} [/math] seconds; assume they have a mass [math] m [/math], then the total distance they would be pushed backward during their jump with respect to the roof of the car would be [math] F_dt^2/2m [/math] or [eqn] \text{distance pushed backward by air resistance}=\frac{C_d A\rho v^2h}{2mg} [/eqn]
I will leave it to you to plug in values! Hint: A is about 0.7 square meters.
>>11396764
>What about using partial derivatives?
Not sure what you mean. You use partial derivatives when you propagate error. Say you have a calculation that depends on N measurements [math] f(x_1,x_2,..,x_N) [/math] and each measurement has an uncertainty [math]u_i[/math]. Then to a first order approximation, the total uncertainty of [math] f [/math] is [eqn] u_{total}=\sqrt{\sum_{i=1}^N\Bigg(\frac{\partial f}{\partial x_i}u_i\Bigg)^2} [/eqn]

>>11396758
Thank you anon!

Can someone pretty please post that meme book chart for category theorists? I think it was kinda pink with anime girls on it.

>>11396943
It's on the good charts folder in the sticky.

Mycology question....

What are the wastes created by mycelium of the higher basidiomycetes, from there digestion process? What are the acidic toxins that build up that make spent mushroom substrate spent? Google has failed me. All I've learned thru searching is that there are toxins, and they are toxic to the mushroom.

Say I have a circle that has a diameter of 10. How do I figure out that math for a point at say 4,4? Do I need to use the same "circle math" for the point but use the new radius (which would be 8?)? How would the math for the r=8 circle compare to the r=10 circle?
I'm sure this is a stupid question but I haven't done math like this in a very long time.

>>11397056
>How do I figure out that math
???

>>11397058
Sorry, I'm trying to figure out all the math I can learn about a certain point. Just different ratios and stuff so I can see how the numbers differ.
How does the sin, cos, tan, etc. differ from a circle with a radius of 10 -vs- a circle with a radius of 8. I'm trying to see the difference.

>>11397072
>all the math
This is very vague, you will have to be more specific with what you want to know. Trigonometric functions don't care about the radius of the circle you are working with. They are defined in exactly the same way.

>>11397080
Basically I'm trying to figure out some math that will show a difference between two points. So if the first circle has a r of 8, imagine a point at (4,0). A second circle has a r of 10 and the point (5,0) exists on that circle. I'm trying to find out some math that will show...something, anything really. Something that shows the math from the first point is smaller than the second point.

What's the effective temperature range where you can stay warm just by wearing a ton of layers or sitting under a bunch of blankets? I sometimes see homeless people with like ten blankets over them in the winter, is that actually enough to keep them warm?

>>11397056
>>11397112
Literally too much to explain.
My bad, but this isn't something I can help with through the internet.
Read Euclid and some text on analytic geometry.
>>11397210
>What's the effective temperature range where you can stay warm just by wearing a ton of layers or sitting under a bunch of blankets?
Any temperature, with enough high quality layers.
Essentially, your body constantly produces heat (because humans are mammals) but you usually lose some of it to the environment. Layers (to an extent, naturally) thermally isolate you from the environment and prevent loss of body heat, which lets you gradually warm up.

>>11396813
thank you for the adorable gifs anon, they are all cute and make my day <3
also just noticed a mrs. brisby poster >>11389885 incredibly based

so as to not shit up the thread, i've been getting more into chemistry lately out of natural interest. I remember from school that molecules react with each other to lower their energy states. I find that incredibly vague; Is there an actual equation that can broadly describe energy states of two atoms and compare it to the energy state of an actual molecule?

Hey, /sci/. I'm currently working on a proof for abstract algebra, and I have a question about operators:
Is it wrong for me to assume (z^-1 * x^-1 * (xz)) = (z^-1 * x^-1 * x * z) if associativity hasn't been proven?

My mind is mush.

I did a, and that was fine, but I am completely clueless with part b. It doesn't make any sense to me.

(a) Show that if G is a group and x has finite order m, y has finite order n,
and x and y commute, i.e., xy = yx, then xy has order dividing lcm(m, n),
the least common multiple of m and n.

(b) Give an example of the result obtained in (a) failing when x and y do
not commute.

>>11397375
Yes.
>>11397379
Set [math]G[/math] as the free group generated by [math]\{a, b}[/math], and modulo out [math]a^2 = b^2 =e[/math], where [math]e[/math] is the identity.
ab has infinite order.

>>11397390
>>11397375

Why would that be the case? Thinking in terms of exponentiation (which isnt necessarily associative), x^y^z = x^(y^z). I'm not changing the order in which the terms are evaluated by the operation.

>>11397413
sorry, I meant to say "which isn't associative". drop the necessarily

>>11397375
>nonassociative structures
do you hate yourself?

>>11396222
>You can be shocked by a single phase at low voltage too
No, I mean by ONLY the phase without a connection to ground or any other sort of voltage dump. You can’t be shocked by a single phase at low voltage since if you’re not grounded you’re simply brought up to the same potential as the voltage source, therefore there’s no difference anymore between you and the voltage source, therefore the current is zero. This is pretty obvious, no electrician would ever be able to work live, high or low voltage, if this wasn’t the case.
> Humans don't make great capacitors.
But everything is SOME kind of capacitor. That was the entire point of my question, would a high voltage of say 250k be enough to give you a sensible shock (around 5mA of current). If you’re ONLY grabbing a single phase, then the only current you should experience should be from being brought up to potential (and discharged), which is just another way of saying capacitance.

>>11397413
Because the one on the right reads [math]((z^{-1}x^{-1})x)z)[/math].
You need to understand that a magma has no rigidity. You cannot prove literally anything for an abstract magma, because it's literally just a fucking set [math]X[/math] with a map [math]f: X^2 \rightarrow X[/math].

>>11396813
why does that formula look so similar to the arc length integral?

>>11391785
I have autism and lots of free time

>>11397390
>free group
We haven't done free groups yet and I don't want to be accused of cheating.
Is there a good example for stupid people like me?

>>11397431
Yeah I caught my mistake. Final question:
I understand that (ab)^-1 = a^-1 b^-1. Then can I say that y*(y*z)^-1 = y*y^-1*z^-1? Or is this still invalid?

>>11397472
Oh yeah, and if it wasn't implied, an identity element does exist.

>>11397457
There's a nice and easy counterexample in [math]S^3[/math].
>>11397472
Literally anything is literally anything.
The result [math](ab)^{-1}=b^{-1}a^{-1}[/math] requires associativity to prove.
Specifically, you make a passage [math](b^{-1}a^{-1})(ab)=(b^{-1}(a^{-1}a))b^{-1}[/math]

>>11397486
>There's a nice and easy counterexample in S^3
I think I'm going to use [math]\mathbb{Q}_8[/math], or is that what you meant?

>>11397515
err, [math]Q_8[/math] I meant.

>>11397515
No, you can give a cycle as a product of two transpositions.
Transpositions have order 2, cycles have order 3.
That probably works, too.

Why is there a multiplication by five? I thought you should just divide by ln 3

In the quantum eraser experiment, is the pattern produced on the film while the eraser is active, a pattern of two lines? It has to be right? Or else you have a probabilistic chance to invoke retro causality.

>>11397210
I will be more quantitative than that other guy. The physical principle at play is Fourier's law, which states that the heat flux conducted through a material is proportional to the temperature gradient over that material. The human body dissipates heat at a rate of something like ~200 Watts/square meter. If you cover your whole body with a blanket, you are putting thermal resistance between yourself and your surroundings. Say you have a blanket that has a thermal conductivity of 0.05 W/m*K (typical) and a thickness of 1 centimeter. Say you want to find the lowest temperature you could exist in such that you can maintain a (surface) body temp of 37 degrees C. Then, 37-T=(200*0.01)/0.05 so T = -3 degrees C or a little below freezing. The is an extremely simplified model that does not consider the still air trapped between your body in the blanket, or any notion of wind or convection. These would tend increase and decrease the possible temperature differential, respectively.
>>11397319
yw <3
>mrs. brisby poster
also me
>>11397425
>without a connection to ground
Sorry, I misunderstood. Ideally, if you are not grounded and grab one hot wire with one hand, you hand is more or less just going to be at a constant voltage. This assumption falls apart at very high voltages because real wires have finite conductivity, and there will be a voltage drop over your hand. Current then flows through your hand per Ohm's law. There's a reason why HV workers wear Faraday suits.
>>11397440
Does it? It reminds me more of root-mean-square.

>>11397210
I will be more quantitative than that other guy. One physical principle at play is Fourier's law, which states that the heat flux conducted through a material is proportional to the temperature gradient over that material. The human body dissipates heat at a rate of something like ~200 Watts/square meter. If you cover your whole body with a blanket, you are putting thermal resistance between yourself and your surroundings. Say you have a blanket that has a thermal conductivity of 0.05 W/m*K (typical) and a thickness of 1 centimeter. Say you want to find the lowest temperature you could exist in such that you can maintain a (surface) body temp of 37 degrees C. Then, 37-T=(200*0.01)/0.05 so T = -3 degrees C or a little below freezing. The is an extremely simplified model that does not consider the still air trapped between your body in the blanket, or any notion of wind or convection (then you need to invoke Newton's law of cooling and do some really fucked up stuff to find convection coefficients). These would tend increase and decrease the possible temperature differential, respectively.
>>11397319
yw <3
>mrs. brisby poster
also me
>>11397425
>without a connection to ground
Sorry, I misunderstood. Ideally, if you are not grounded and grab one hot wire with one hand, you hand is more or less just going to be at a constant voltage. This assumption falls apart at very high voltages because real wires have finite conductivity, and there will be a voltage drop over your hand. Current then flows through your hand per Ohm's law. There's a reason why HV workers wear Faraday suits.
>>11397440
Does it? It reminds me more of root-mean-square.

>>11397528
Oh, yours is much better, thanks for the help. Really needed it.

>>11397594
>This assumption falls apart at very high voltages because real wires have finite conductivity, and there will be a voltage drop over your hand
This is irrelevant for any realistic transmission voltages isn’t it?
> you hand is more or less just going to be at a constant voltage
It won’t be though. It’ll follow the same variation as the phase you grab. You’ll be continuously be brought up to max potential then down to 0 60 (120?) times a second. By definition this means some kind of current is running, I just don’t know how much since humans are poor capacitors.

>>11397554
3^(x/5)=exp((x/5)*log(3))=exp(log(3)/5*x) and the integral of e^(kx) is e^(kx)/k (k is not 0)

>>11397646
>This is irrelevant for any realistic transmission voltages isn’t it?
I don't think so. I'm pretty sure you're in trouble if you touch a HV line with your bare hands even if you are not grounded.
>phase
I don't think this means what you think it means. Any single wire can only transmit one phase at a time. Three phase transmission requires three cables (plus one for neutral).
>capacitance
For an entire human, the capacitance is in the order of 100 picofarads. For your hand, it is even less. When you put your hand on a live wire, it is like you are putting a pretty decent resistor and an absolutely tiny capacitor (your hand) in parallel with an absolutely tiny resistor (the transmission line) that happens to have a lot of current thru it. The capacitance is irrelevant. At high frequency, the impedance of the capacitative part of your hand drops and the total impedance of your hand drops as well. More current flows through you and you get a bigger zap.

>>11397594
>smarmy faggotry
Called it.

>>11397708
>I don't think so
I CBA to do the calculations and get an exact value, but it obviously is. A voltage drop of even a few volts over, generously, a few feet let alone the width of your hand would mean you’d have massive voltage drops over even intercity distances. Not the mention actual intercity lines would be way lower voltages and therefore much higher loses.
>don't think this means what you think it means
I don’t think you understood the very obvious implication there which probably means you shouldn’t have tried answering this question... The fact that it’s a phase at all means alternating current. Yes, you’re only dealing with one phase. No, that doesn’t mean voltage is constant.
>For your hand, it is even less
Why the hell is this relevant? Your hand isn’t isolated from your body and if it was then getting shocked is a pretty meaningless statement.
>The capacitance is irrelevant
How is it irrelevant? It’s quite possibly the only relevant source of current at the 6 figure voltage level when there is no voltage dumpster involved.
>More current flows through you
Define the sources of any current at all. Again, the only one I can think of is from electrons flowing in and out of you as you’re kept at the same voltage level as the power line. With a capacitance of 100 picofarads and a max voltage of 250k ish volts I don’t know if the total current is all that high (high being milliamp range), and that is my question.

You’re worse than unhelpful. It’s like you’re trying to google to answer questions people ask with no prior understanding and now I’m forced to explain really simple concepts you should have know before answering the question.

Why do nonzero quaternions necessarily have a multiplicative inverse?

>>11397792
because quaternion units form a group. we know it's a group because of the relations of quaternions we defined to be quaternions.

>>11397796
Thanks. I just realized how fucking rarely I remember definitions. Need to work on that.

>>11397786
>put both terminals of a capacitor at the same voltage
>"guys how much current goes through it"

>>11397796
>every group ring over the reals is a division ring
Does it really be like that?

>>11397281
>Literally too much to explain.
I don't need a dissertation on math, I just need a single equation.

>>11397792
I can't argue the underlying theory, but you can derive a formula for the multiplicative inverse of an arbitrary nonzero element of the quaternions. This is similar to the formula for the multiplicative inverse of an arbitrary nonzero complex number.
Suppose we are given nonzero q=a+bi+cj+dk. If p = a -bi -cj - dk, the product pq is a nonzero real number a^2 + b^2 + c^2 + d^2. Thus p * (1/(pq)) * q = 1.

>>11397859
Area of circle with radius x compared to circle with radius y is (x/y)^2 * area of circle with radius y.

>>11397820
It really do be like that sometimes.

wish i tried hard in high school or undergrad so i could go to an ivy league

Why is the definition Cartesian product of sets different than that of functions?
Aren't functions just sets? How do I distinguish them?
Let f be a function from S to T, g a function from U to V.
Is the product of f and g the set of all ordered pairs (x, y) where x is an element of the product of S and T and y an element of the product of U and V, or the set of all ordered pairs (z, w) where z is an element of the product of S and U and w an element of the product of T and V?

does a prime number have four factors because it has itself, 1 and the negative versions of those numbers?

What's the maximum number of sides an equilateral shape can have in an endless repeating pattern?

I have a feeling it's 6 but maybe there's more.

Beyond lost on this, please help it's due in a few hours

>>11398270
Typically when defining primes we look only at natural numbers, not integers.

>>11398423
chain rule

what controls skull shape? is it shaping itself around the brain or do they grow independently?
can you have a normal looking skull but have voids where it doesn't meet the brain?

>>11398596
>what controls skull shape
Race

>>11388817
Is this proof correct?

>"Prove that the empty set is a subset of any set"
> Let [math]A[/math] be a set
> We know that if [math]B[/math] is also a set then [math]A \cap B \subseteq A[/math]
> Let [math]B = A^c[/math]
> Then, by definition of the complement, [math]A \cap B = \emptyset[/math] and [math]A \cap B \subseteq A[/math], thus [math]\emptyset \subseteq A[/math]

>>11398720
Obviously genes are involved but how? is the skull shaping itself to the brain? or are the brain and skull developing in a coordinated way?

>>11398759
It's not correct, because the complement of a set is not well defined unless you specify the superset.

New Question.
Family history says my father's-father's-father's, etc., back to 1650 came from France.
Our last name is French.
So it stands to reason (I think) that my Y chromosome (recombination aside) comes from France.
But my Dad got a DNA test, and they say he's almost entirely Irish, with no trace of French.
I know, that sounds like a vast oversimplification, but my real question is this:
Was there an Irishman in the woodshed?
Does his DNA test indicate the family genealogy is wrong?
Presumably because one of my female ancestors cheated on her husband?

I ran into a rock ledge and hit my knee full impact running into a rock. and also hit the area below my knee to the side a bit. Can this cause a blood clot?

When walking up a steep hill I felt a mild to annoying pinching pain in my ass briefly. What was that? Can that cause perferorations or blood clots.

I just did mushrooms and went for a hike

Is there not a way to convert co2 into a stable solid on a mass scale like trees do to solve global warming. It wouldn't have to be as energy dense as the oil product it came from just enough to capture it into a solid. Even less so than a tree. Then could you not just write it off as a drop in efficiency of a coal /gas plant or engine if it was say 5% or so. You can just fill all the mines and drill sites that the carbon gathered from in the first place with the solid.

>>11398951
>Is there not a way to convert co2 into a stable solid on a mass scale like trees do
Yeah.
Trees.

>>11398957
But more efficient and faster than trees. That would convert it as fast as it is produced. With a smaller footprint aswell like an addition to a powerplant rather than millions of trees

Hi /sci/sqt/
I'm getting ready for a calculus test and today I am working on the partial fraction decomposition. Some questions will require me to complete the square in the denominator. When they do it here in the book, they get a more convenient solution to work with than I do. Can anyone point me in the direction to getting the result that they get when completing the square? I can prove that their answer is equivalent to mine, but I don't know how they got theirs

>>11398875
Cracking your knuckles can give you a blood clot stop doing drugs you retard

When people say their hair is "Getting thinner", what are they referring to? Are the hair strands themselves getting thinner, or are they saying that the density of hair on their head is decreasing?

>>11398979
Density

>>11398979
hair follicle density.

If you standardize all data in a Normal distribution using z-scores, what is then the mean and standard deviation of that distribution?

>>11398865
No that's not how it works

>>11399030
OK, you got more than that?
I'm happy to believe I'm wrong, but my logic goes like this:
I only inherited my Y chromosome from from my Dad, as he did from his Dad, etc.
How did I get an apparently Irish Y chromosome?

>>11398973
Can't help much if you don't post your solution. HD non-retarded copy of the page btw.

>>11399073
Thanks for that.Im sitting at work on my day off cause its easier to study here than at home

When i complete the square I am getting (x-1/2)squared + 1/2. The book is getting (2x-1)squared plus 2.

>>11399164 here
So i am guessing that they got the same result but wanted to remove the fractions, so when they multiplied 2 in the parentheses, they had to do it twice because of the square. So instead of multiplying 1/2 outside the parentheses by 2, they are multiplying 1/2 by 4. Is that what is happening?

>>11399073
What's the book name?

>>11399327
Calculus early transcendentals by stewart. Eighth edition

Can hearing damage be prevented fully if you shoot constantly with hearing protection? Seems like the limit of hearing protection is around 36 NRR with just earmuffs and plugs which is not even 15 decibels. Given a 9mm is around 155, is the best you can hope for to reduce the damage?

>>11398759
>muh neat trickery
Just apply the definition.
>>11398865
>my son, you are wondering about heritage, must choose reliable source of information
>will you trust your family, who has raised you and loved you, to tell you about its own history
>or will you send your foreskin and 50 bucks to mister Shekelberg in the mail, who will use them to perform strange hebraic magicks, make up something and send it back to you?

I'm pretty lost.

>Calculate how many 3-digit numbers with different digits can be made up of the digits 2, 3, 5, 6 and 7. How many of them are greater than 400?

The first part is easy, 5P3=60

But the second one?
I tried fixing the first, and then seeing how many permutations I can make with the others, so 5P2=20. But this is not the way to do it obviously.

Any clue?

>>11399515
If it's smaller than 400, it either starts with 2 or 3. Then, we have to choose the remaining two digits out of four available options.
And then we're done.

>>>/n/1452207
>the energy stays proportional to the mass without affecting the speed. we can ignore friction when only comparing the weight assuming the bikes have similar aero and the rolling resistance of the heavier bike could be adjusted accordingly by giving it a higher tire pressure.

>>>/n/1452225
>Two marbles with different weight but equal diameter will roll down a hill equally fast in a vacuum.
>On earth, the heavier marble will be faster because it has more potential energy stored to overcome the aero drag. The aero drag increases with a cubed correlation to speed so it is very significant.

who's right

also how does buoyancy relate to all of this?

>>11398865
I think your DAD might not be the one you think he is,
youll have to speak to your mom about this one

>>11398865
couldn't it be like this
>irishman moves to france some time before 1650
>has children
>etc
and jeez i wish i could trace my ancestry like that, are you noble or famous or something

I'm taking electronic circuits this semester and a couple weeks in, I have no idea what's going on, where do I start?

>>11399785
They are both saying things that are correct, and I don't really care to read the entire conversation. Drag force varies with the square of velocity, btw, and bouyancy is so tiny that it basically doesn't matter and you can neglect it entirely.
>>11400165
What don't you understand? Intro circuits is pretty easy.

How do we/scientists know that CO2 is the problem that drives global warming and not something else?

Is it possible to execute Shor's algorithm using a the ripples in a really big pool of liquid?

>>11388817
If I have a recursive function that describes a_n in terms of a_1, a_2, .... , a_(n-1), what do I call that? I want to call it a recurrence relation, but according to the definition here:
https://en.wikipedia.org/wiki/Recurrence_relation#Definition

it seems that a recurrence relation must have a fixed order k. Whereas, as I've described it, the "recurrence relation" would have an order of (n-1), and therefore vary with how far along in the sequence we are looking. I'm having trouble finding examples like this, and I think if I just knew the name of it and/or had the proper vocabulary for it, it would be much easier to google.

brainlet here someone explain Schrodingers cat to me. i dont understand why it is a thing

What are some standard position titles you find in industry research goups?
At my work we have Program Manager, Chief X, Senior X, Research Scientist, Research Associate, Research Assistant
Then non-research positions there's Lab Manager and Lab Technician.
When I look at job ads they have different titles or same titles for different seniority levels. Makes shit hard to compare.

>>11400793
It's just a thought experiment to illustrate how crazy quantum mechanics can be, even though in reality it would require a magical box that prevents all information from leaking.

Quantum mechanics has a bit of a philosophical issue in regards to interpretation what happens when the wave function "collapses". That is, nothing in quantum mechanics describes when or how a particle goes from being a stochastic wave to a single-point interaction. The many-worlds interpretation says that the wave function never collapses because everything just diverges into alternate worlds, but then that brings up the question of where do we get probabilities from? If every possibility gets its own universe, then what does it mean for one universe to be more "likely" than another one? The many-worlds interpretation is a type of determinism.

The Copenhagen interpretation, which is what is happening the the Schrodinger's cat thought experiment, states that the wave function DOES collapse, we just don't know when or how.

>>11400793
allegory for the crazy behavior of electrons, among other things

What the fuck do I do here?

>>11400340
dunno, i'm skeptical, and i think economic growth and scientific advancement is more important so that we shouldn't cuck ourselves too much, like if we colonize mars then we won't need earth anyway, and electric cars aren't as clean as people think, the mining process for the rare earth minerals causes pollution, and we'll be dead anyway by the time the climate has changed too much, the imminent doomsday scenarios are a hoax
>Without new policies to mitigate climate change, projections suggest an increase in global mean temperature in 2100 of 3.7 to 4.8 °C, relative to pre-industrial levels (median values; the range is 2.5 to 7.8 °C including climate uncertainty).[24]
https://www.youtube.com/watch?v=PLxPAwIeL0w
https://www.youtube.com/watch?v=Hatav_Rdnno
https://www.youtube.com/watch?v=oJL9MasBFvM

I'm really stupid but.

If I have a 0,04% chance of something happening, and I add it's 20%, what are the odds of that event to happen, 1 in how much. Help I have retardation.

Is it douchey to frame your diploma?

>>11401126
I have no idea why people do this. Unless it's to offer like confidence to your patients or the people in your office.

>>11401126
If you have an office and need to take clients, no, but I personally would never hang it up in my house. But really if it's something you're proud of and want to display, there's nothing wrong with it necessarily, and if you're having people over to your house hopefully they know enough about you not to judge you unfairly by it.

i search for news on autism on Google everyday. do you think well ever get a cure?

>>11396684
Cute.
>>11400839
This is a pretty archaic/naive interpretation. The amount of (quantum) information contained in a state [math]\rho[/math] is given by the von Neuman entropy [math]S = -\operatorname{tr}\rho\ln \rho[/math], which is minimized for pure states, so we [math]do[/math] know how a state collapses: it's when [math]S[/math] achieves a minimum. Schrodinger's cat never was an objection because it never took into account the localization/decoherence of the quantum dot when it couples to the massive classical heat bath (cat), which is described quite well by the thermalization hypothesis.
>>11400914
Let [math]G=(V,E)[/math] be a graph, we know a few things:
1. [math]|V| \geq |E|[/math], since two ,
2. [math]|V| = |\tilde{F}|[/math], where [math]\tilde{F}[/math] are the faces of the dual graph [math]\tilde{G}[/math],
3. Euler characteristic [math]\chi(G) = |V| - |E| + |F| = -2 = \chi(\tilde{G})[/math] for planar graphs [math]G[/math].
What these mean is that a degree sequence [math](d_i)_i[/math] is graphic if [math]\sum_i(2 - d_i)\leq -2 [/math] since [math]|V| = \sum_i[/math] and [math]|E| \leq \sum_i d_i[/math].

>>11401251
>1. [math]|V|≥|E|[/math], since two ,
Unfinished, unnecessary and untrue. I'm retarded lmao.

What is your opinion on "Calculus: Early Transcendetals"? Is it a better choice for someone who forgot almost all of precalc than Spivak or Apostol?

>>11401178
autism is a personality traint, you cant cure a persons personality. what we need a cure for is a society that overvalues social skills.

>>11401535
Impossible, for valuing personality skills is itself a personality trait.

>>11401535
Impossible, for valuing social skills is itself a personality trait.

Why are steroids illegal? I can understand for athletes, being sportsmanlike and playing for the spirit of the game, and all that shit. But what about your average John Doe? Aren‘t steroids basically like „biohacking“ too, shouldn‘t we be researching that shit hard af? We aren‘t ever gonna become awesome cyborgs if we aren‘t allowed something as rudimentary as affecting our enzymes or whatever.

>>11401574
Lots of negative side effects when abused, easy potential for serious health issues and possible death. Same reason a lot of diet pills aren't legal. Your average brainlet would fuck up and kill themselves. People already manage to do it every couple weeks with access to shit like caffeine and nicotine.

>>11401574
https://www.youtube.com/watch?v=CbSzPwzFVVQ

I was attending computer science lecture and felt that vague sense of 'tism' from the whole lecture's atmosphere

>>11401724
Did you like it?

>>11401724
Did you also feel any vague sense of what the lecture was about? Could have been quantum computing, which would adequately explain it.

>>11401724
what I mean by tism is autism lol
>>11401766
yes, it was fun
>>11401779
no, it was some basic shit really

From the Wikipedia article on split-phase systems,

>Since the two phasors do not define a unique direction of rotation for a revolving magnetic field, a split single-phase is not a two-phase system
I don’t understand how this is a differentiating quality between split and two phase. If in your two phase system you had the two phases separated by 180 degrees wouldn’t that mean that system also wouldn’t have a unique direction of rotation? And if the Wikipedia article is wrong, what is the true way to differentiate them? Would it be wrong to say split phase is not two phase because both connections are to a single transformer (or secondary winding?)?

>>11365784

you might not care anymore but if i!=j then you can split this into two sides - one where i < j and one where j < i. If you assume that it is evenly split between the two sides then you can take one of the halves, in this case i < j, and use it to "double up" in a sense. This leads to x(i)y(j) and x(j)y(i) having all the values from x!=j.

>>11401251
I'm not really allowed to show it like this. Too many definitions we haven't gone over yet, and I don't necessarily understand any of it.
I think it's meant to be a bit simpler.

you guys warned me about diffeq and its ties to linear algebra. I can definitely see how knowing it can be a huge boon in diffeq. Unfortunately I know hardly anything above precalc matrices and even then I've forgotten most of that.

We're doing variation of parameters at the moment. The book says that, via Cramer's rule, you can find the solution to
[eqn]y_1u_1'+y_2u_2'=0\\
y_1'u_1'+y_2'u_2'=f\left(x\right)[/eqn]
given that
[eqn]u_1'=\frac{W_1}{W}\\
u_2'=\frac{W_2}{W}[/eqn]
where
[eqn]W=\begin{vmatrix}y_1&y_2\\ y_1'&y_2'\end{vmatrix};\:W_1=\begin{vmatrix}0&y_2\\ f\left(x\right)&y_2'\end{vmatrix};\:W_2=\begin{vmatrix}y_1&0\\ \:y_1'&f\left(x\right)\end{vmatrix}[/eqn]

I remember being told, and am currently seeing everywhere that Gaussian elimination will always be faster than using Cramer's rule. In that case, is there a faster, easier way to solving a nonhomogeneous higher order linear differential equations?

>>11402198
>>11402198
I forgot to add "easier way to solving a nonhomogeneous higher order linear differential equations via gaussian elimantion"

>https://en.wikipedia.org/wiki/Circular_sector#Area
I hate to ask, but what function is S supposed to represent?

I know in MCNP you can set your source to produce particles in a number of discrete energies. Can you make a distribution of energies? Like say I wanted my source to produce particles ranging from 60-66 MeV.

>>11400914
Use the Erdos-Gallai theorem.

>>11402226
dS represents an infinitesimal 'sector element'

that is the area element where you perturb the radius and angle infinitesimally.

>>11388817
How can I understand electron phase
Can someone give me a brainlet explanation, my autism is preventing me from just accepting that it is a thing and moving on

I'm studying Abstract Algebra and Real Analysis of One Variable simultaneously. In the Analysis book, I found this. Wouldn't this fact be self-evident by understanding that > is an equivalence relation over [math]\mathbb_{R}[\math]

>>11401535
This is literally what is causing ''''autism'''' you turbo autist

Locking children in math and science classrooms for the majority of their formative years is what prevents people from reaching social developmental milestones

I'm asked to find a condition on [math]|x-1|[/math] such that [math]|x^2-1| < 1/n[/math] for every [math]n \in \mathbb{N}[/math].

So, the condition I came up with was [math]|x-1| < 1/4n[/math], because then [math]|x+1| = |x-1+ + 2| \leq |x-1| + 2 < 1/4n + 2[/math] and therefore [math]|x-1| \cdot |x+1| < 1/4n(2 + 1/4n) = 1/2n + 1/16n^2 < 1/n[/math]

I know my answer is right, but I'm wondering, am I expected to come up with a simpler/different solution?

>tfw just wanted to study computer science and I'm here doing calculus 2 for the third time just to get into the program
fuck i want to die

>>11401535
autism advocates will tell you this but it isn't the case. autism isnt just being different, its you being straight up worse at things... your brain is fucked, it isnt functioning like a normal brain would. autism doesnt just fuck your "social skills" it impairs everything with you
pep shouldnt stop to try to make it ok to be an autist but also shouldnt forget it for what it is. autism is a BAD thing

>>11402268
You can’t just use the definition of > since you have no equation given as x > z. Yes, it’s intuitively obvious but that’s not exactly a proof.

how do electrons carry energy and what exactly do resistors do to them to make them have less potential energy? In a water analogy it would be kinetic energy being reduced or water having less pressure. Does it have something to do with orbitals?

Is there such a thing as post modernism in Mathematics?

>>11402226
it's the name for the rdrdo thing after the equals sign

>>11402053
Then I'm afraid your only option is to try to draw a bunch of graphs.
>>11402198
Depending on your function space, differential (as well as integral) operators can be represented as infinite matrices by passing to an ONB, which you can get from either Sturm-Liouville or [math]N[/math]-representation. For instance [math]\partial_x \cong [\delta_{n,n+1}]_{n\in\mathbb{N}}[/math] in the Fourier basis. Notice that these matrices are infinite dimensional, as are most Banach function spaces.
Cramer's rule and Gaussian elimination work for finite-dimensional matrices, but given sufficient regularity/invertibility (via Fredholm alternative, for instance) you can construct solutions via Cramer's rule by just plugging in the matrix entries. Gaussian elimination requires you to manipulate the rows/columns themselves, however, which you of course cannot do infinitely many times. Generally you cannot use induction (i.e. finitely many test cases) to prove convergence statements.

>>11402407
Nah, I found an easier way. Maybe you should cut down your buzzwords per post ratio and think a little more.

>>11402367
In the water analogy, voltage is more like hydraulic head (the sum of static and dynamic pressures with gravitational potential). Kinetic energy (dynamic pressure) is really a very small part of head, and so is the actual kinetic energy associated with electrons. In the water analogy, a resistor would be associated with a rough section of pipe or a change in geometry or a bend, etc., that causes head loss.

how the fuck do I focus and delay gratification? Am I just to much of a brainlet? I was supposed to read and study and install some programs but I totally shit the bed.

>>11402415
That's good to hear sweetie. Sorry I made you feel insecure about what ultimately amounts to common 2nd/3rd year topology knowledge. Not my intention.

>>11401251
>cute
Correct.
>>11401724
What's your question?
>>11402268
> [math]a>b[/math] is an equivalence relation
It isn't.
>>11402352
>a condition for every [math]n \in \mathbb{N}[/math]
Iff x=1.
>am I expected to come up with a simpler/different solution?
I'm pretty sure you're supposed to literally brute force this problem.
[math]|x^2-1| < 1/n[/math] if and only if [math]x^2 - 1 <1/n[/math] and [math]-x^2+1 < 1/n[/math] , because modulus.
Do some algebraic manipulation, get two conditions.
Or split it up in [math]x>1[/math] and [math]x<1[/math], same same.
>>11402373
https://www.springer.com/gp/book/9783662053065
>>11402422
Acquire great anger.

>>11397786
>there is no voltage drop/voltage drop is completely insignificant
>so what happens if I place both terminals of a capacitor at the same voltage
The answer is fucking nothing.
>>11402427
Got his ass.

>>11402419
I have another question if you don't mind. How is voltage reduced(and what does voltage drop really even mean?) if nothing about stream of electrons is changed. They still go the same speed and there is no charge build up as I understand it. I know that resistors take energy from the circuit but energy is just a high level abstraction of what is really going on. So what exactly is changing in the electrons to reflect the lowered potential energy?
Sorry if this question is kind of autistic or I'm missing something obvious. It's been bugging me for like 2 months now.

>>11402367
How they carry energy doesn’t really make sense. They don’t “carry” anything. The energy you can get out of them depends on how you use them. For examples in LEDs they fill electron holes and light is emitted. In motors the current is used to generate a magnetic field that drives it.
>what exactly do resistors do
They impede electron flow more than other materials. There’s nothing magical about resistors. It just happens to be that the arrangement of the material allows electrons to travel less easily. It’s more of like the imaginary line between mountain and mound. They don’t decrease the potential energy, they make the same magnitude force push electrons less quickly.
>does it have something to do with orbitals
Yes sort of. Bad conductors, I.e. resistors, can impede flow because the atoms that make up the material holds on to their electrons tightly. A high enough voltage will still strip the atoms of the electrons and another will take its place. As you’ve probably learned in HS chem, electrons moving around orbitals releases EM radiation. This is why things heat if you run a current through them. In metals the electrons are held very loosely but in other materials, say organic compounds, they are held more strongly and you’re constantly stripping them of electrons.

>>11402268
> being an equivalence relation implies a > b and b > a

>>11402246
Thank you for your answer, but may I ask how exactly one could imagine this area element on the circle? I cannot seem to imagine it at all with the angle becoming infinitesimal.
If it was an integration of the arc length I could visualize it, but that one would be with a constant angle.
>>11402398
Ah yes, thanks, but what is it supposed to represent geometrically?

>>11402352
you can see that |x^2-1| < |x^2+2x-1| which is |x-1|^2
therefore |x-1|<1/sqrt(n) -> |x^2-1|<1/n

so if |x-1|<1/sqrt(n) you're solid

>>11402553
So I think I understand this but what exactly causes voltage drop then?(and what are the physical/intuitive results of the voltage drop?) Nothing changes about the current or charge density anywhere.

>>11402579
btw this assumes x is always positive

>>11402530
>How is voltage reduced(and what does voltage drop really even mean?) if nothing about stream of electrons is changed
I'll go back to the water analogy. Suppose you've got a simple pipe network. The fluid (water, for example) starts at A and terminates at B. The hydraulic head at A is equal to the hydraulic head at B, plus whatever head is lost in the pipes, minus whatever energy was imparted to the fluid by your pump. (hA=hB+hL-hP). Here, hP is like the batter in a DC circuit, and hL is like the voltage drop over a resistor. Energy is definitely lost to friction and geometry changes in the pipes, but the volume and mass flow rates (analogous to current) are exactly the same everywhere in the pipe network, including at A and B.
>So what exactly is changing in the electrons to reflect the lowered potential energy?
I'm honestly not sure, but it isn't necessary to consider individual electrons to analyze or understand electrical circuits. A resistor is just a section of a the circuit that has very high resistivity. Resistivity is an intensive material property and a function of the material's temperature. There is something called the free-electron model, I suggest researching that.

>>11402573
Here read this
https://en.wikipedia.org/wiki/Solid_angle

>>11402612
I think I have a better understanding. Thanks for the answers.

>>11402591
The total hydraulic energy in a moving fluid drops over lengthy sections of pipe, and yet nothing changes about its mass flow rate or mass density anywhere. Voltage drops because there is an electric field present in a resistor.
>why
Because of Kirchhoff's loop law (which is just the conservation of energy), any voltage increase (like from a battery) is balanced by a voltage drop.
>so why doesn't the voltage drop in the wire and not the resistor
Because in basic circuit analysis you treat the wires as if they are ideal conductors. It is a fact that ideal conductors are potential surfaces.
>>11402627
yw

>>11402591
The total hydraulic energy in a moving fluid drops over lengthy sections of pipe, and yet nothing changes about its mass flow rate or mass density anywhere. Voltage drops because there is an electric field present in a resistor.
>why
Because of Kirchhoff's loop law (which is just the conservation of energy), any voltage increase (like from a battery) is balanced by a voltage drop.
>so why doesn't the voltage drop in the wire and not the resistor
Because in basic circuit analysis you treat the wires as if they are ideal conductors. It is a fact that ideal conductors are equipotential surfaces.
>>11402627
yw

>>11402573
I will have to learn more to understand that one, but thank you my friend for guiding me into the right direction!

>>11402591
Correct me if I’m wrong but you seem to think voltage is a measure of potential energy. It’s not. It’s called potential difference because the difference in potential creates a force, so voltage is a force. If your house is at 70 degrees and outside is 80 degrees, would you say anything is at a temperature of 10 degrees? The voltage drops because, obviously, resistors resist this force. If they resist the force, obviously the force isn’t as great as on the other side. Think of the difference between shoving someone directly and shoving them by pushing the lead table they’re leaning on.

What's the scientific consensus on incels?

>>11402930
femcel cope

>>11402573
I think of the radius part as the height of a triangle and theta as the number of those triangles

Do high energy neutrons really "bounce off of" nuclei they collide with, or do they just get absorbed and re-emitted?

>>11402476
Excel it’s not nothing, because the voltage is constantly changing. What do you think happens when one side of the line is at 249,999 volts and you (the capacitor) are still at 250,000? I don’t know, you’d probably have to ask someone as supremely qualified as a high school physics student what happens when there is a potential difference but I have a feeling the answer isn’t “fucking nothing”.

>>11403074
>talking about voltage as if it is magically defined at a point in space
>thinking a voltage drop from 300 kV to 299.999 kV is physically different from 3 V to 2 V
The difference in potential is 1 volt, or two volts if you are talking peak to peak. The frequency is ω. You have an R and C in parallel with this potential. Go and solve it.

can someone explain to me the concept of a generalized function in a not too mathematically tigorous way? I understand it's like a function whose input is another function, but I can't fully grasp the concept. And then doing stuff like finding out the derivative of the dirac delta just totally confuses me

>>11403156
>what's a distribution
An extremely well-behaved linear functional on the space of test functions.
Well-behaved in the sense that it can be locally "bounded above by the supremum of some differential operator or the identity (colloquially known as the trivial differential operator)."
So, for example, the dirac delta of a function is everywhere smaller than the function itself, and thus it's a distribution.

>>11403098
D-did you really not understand the sarcasm in the last post? It’s very obvious what happens when there’s a potential difference.
>thinking a voltage drop from 300 kV to 299.999 kV is physically different from 3 V to 2 V
Again, the utter lack of understanding of even the basics of the question is just making you look more and more retarded every time you try to be a smart ass. Again, we are talking about alternating current. A system that oscillated between 300k and 300k-1 might as well be DC. My point was about the micro second to micro second interaction, as there’s very obviously a current. The system itself will oscillate between 300k and -300k.
>The difference in potential is 1 volt
No you dolt. It was just a very basic example. The human and the line will variate almost equally I would assume, and you certainly wouldn’t know any better to correct me on that.
> You have an R and C in parallel with this potential.
You don’t even seem to understand what a capacitor is. You know R is infinite when the voltages are equal right?
>in parallel with this potential
There is,probably, no meaningful circuit in parallel. Given your last answer, you agree with this. Unless of course you were talking out of your ass.
>Go and solve it.
it’s funny how smug you were acting just a post ago about obviously nothing happening, now after looking like an idiot you want to give a random set of variables that don’t even fit and tell me to solve it? So which is it? You’re a clown. Maybe stop trying to answer shit you don’t even comprehend and you won’t look like one so often.

The relevant calculations are this. Someone tell me if I’m wrong, but please not one of these cutesy posting faggots who think they’re going to answer every question here with their google-fu.
q=C*v * 120 per second so a person grabbing a 250k 60 hertz line would experience a current of 3mA.

is there anyone who understands intuitively why complex numbers work like a circle when graphed? its too weird.

also why does -1 times 0-1 equal 1

>>11403437
>why complex numbers work like a circle when graphed
In what way? They work just like any other number if you mean on an imaginary axis, which you probably don’t.

>>11403437
it works like a 2d rotation matrix

>>11403437
https://betterexplained.com/articles/understanding-why-complex-multiplication-works/

>>11403437
You mean de Moivre's formula?
Basically, because any nonzero complex number can be given as a double of a positive real and an element of the complex circle [math]S = \{ z \in \mathbb{C} : |z|=1 \} [/math], and the only topological group structure that the circle admits is angle addition modulo 360 degrees. Shitty source for the second result here https://math.stackexchange.com/questions/2349439/topological-groups-on-the-circle-s1

Think of it like this: you have the complex circle [math]S[/math]. You know it's closed under multiplication, and that [math]1[/math] is the multiplicative identity. Try to come up with another continuous multiplication, and notice how it "kind of preserves order", so you can "torsion it back into angle sum".
>can't you give an explanation that doesn't assume basic calc and group theory
No.
>>11403471
>assumes the reader understands why multiplication rotates by 90 degrees
Very nice, tho.

Are mass and potential energy the same thing?

>>11403494
>assumes the reader understands why multiplication rotates by 90 degrees
start with these
https://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/
https://betterexplained.com/articles/intuitive-arithmetic-with-complex-numbers/

>>11403471
(1+i)(-1+i)

means you make two vectors out of one and then add them. the first vector is a scaled one and the second one is a rotated one. Adding a Qxscaled V with a Qyrotscaled V is equivalent to rotating V and scaling V by Q's angle and magnitude.

but why ? its too perfectly circular.
Thinking in terms of eulers formula as the axiom might make it easier but why is that true other than differentials locking into place?

>>11403033
Quantum mechanically they are scattered off the atom. Some weak interaction (like [math]n\rightarrow p+ e^-[/math]) must occur in order for the neutron to be absorbed, but this typically doesn't happen unless at quite high energies.
>>11403156
Given a measure space [math](\Omega,\mu)[/math], historically the space of generalized functions is the [math]L^2[/math]-closure of [math]C^\infty_c(\Omega)[/math], or a sequence [math](\varphi_n)_n\subset C^\infty_c(\Omega)[/math] such that [math] \int_\Omega \varphi_n^* f\rightarrow \int_\Omega \varphi^* f < \infty[/math] for all [math]f\in C^\infty_c(\Omega)[/math]. Depending on the measure [math]\mu[/math] and properties of the measure space [math]\Omega[/math], this is subtly different from the modern understanding of distributions as the topological dual [math]\mathcal{S}'[/math] of [math]\mathcal{S} =C^\infty_c[/math] (which is what you are thinking of when you say "it's like a function[al] whose input is another function"), however, as not all distributions are generalized functions, i.e. not all distributions admit a representation as an integration. You typically need [math]\Omega[/math] to be at least paracompact and finitely measurable.
In addition, how "nice" (in terms of its regularity) [math]\mathcal{S}'[/math] is depends again on the measure space as well as the topology (weak-, strong- or Mackey) you endow on it. For certain spaces they can very different. It'd be a slight misunderstanding to say that "distributions are [...] 'well-behaved' functionals" (quotes mine) since they are by definition the entire linear dual; their regularity is controlled by the topology you endow, not by how you artificially pick them out.
>>11403437
The algebraic (multiplicative) properties of [math]\mathbb{C}[/math] are endowed from those of [math]\mathbb{R}[/math] by taking the algebraic completion. The polar representation then falls out like a stillborn.
>>11403504
No.

>>11403512
>polar falls out like a stillborn
But its too weird. like the algebra works but how would you ever expect that happening . WHy the fuck are numbers a circle???

one thing i thought of would be trying out alternative algebraic models like not using imaginaries but defining some other second dimension term that acts differently, and seeing how it graphs out, but idk what to try

>>11403508
with real numbers you can scale and you can rotate by 180 degrees with multiplication
with complex numbers you have an extra dimension so you can rotate not just by 180 degrees

>>11403524
it makes sense for just multiplying by i. but its weird that it should hold for every angle

>>11403520
This anon >>11403524 does raise a good geometric point:
[math]\mathbb{C} = \mathbb{R}\otimes \mathbb{C}[/math] is the complexification, so their isometry groups [math]\operatorname{Isom}\mathbb{R}_\mathbb{C} \cong \operatorname{Isom}\mathbb{C}[/math] are also complexifications of each other. If we just strip away the translations we have [math]O(1)_\mathbb{C} = (\mathbb{Z}_2)_\mathbb{C} \cong SO(2) = U(1)[/math] so inversions in [math]\mathbb{R}[/math] becomes the circle group under complexification.

>>11403531
first of all. i dont know what those symbols and words mean. second of all
>circle group
but wy its a circle?

>>11403535
Because if [math]z_1, z_2 \in S[/math] we immediately have [math]z_1z_2 \in S[/math].

>>11403535
Well rotations in [math]\mathbb{C}[/math] are by definition parameterized by a circle

>>11403525
each extra dimension contributes to more complexity
if you have 0 dimensions so it's just a point, that's a lot lamer than a 1 dimensional number line, and then it's another big leap to the 2nd dimension and so on

https://www.youtube.com/watch?v=Q_B5GpsbSQw

>>11403538
that assumes to be true that i am inquiring for the rationale behind, i think

>>11403539
so?

>>11403542
so 2D means more space, but more space doesnt inherently imply circles should fall out. why doesnt the complex multiplication result in some weird spiral?

>>11403544
So [math]U(1)[/math] is a circle...

>>11403546
i dont know what U1 is mate.

>>11403544
It does fall into a sort of weird spiral for norms smaller than 1 or larger than 1.

>>11403551
Group of rotations "mate"

>>11403552
ok, how about we ignore the norm and say the angle moves in pulses instead of additively. like angle 30 * angle 45 goes to 90. or someshit. but it dont

>>11403560
See >>11403494

>>11403556
man whats some group got to do with FOILing some numbers with a weird trait

>>11403566
Man what's some group gotta do with group operations????

>>11403319
>You know R is infinite when the voltages are equal right

>>11403544
it's "flat", so like imagine if you have a 2d image and you can place the coordinate system wherever you want in relation to the image, the multiplication by i will be a 90 degree rotation around the origin, now you can rotate the image or the coordinate system and it will still work, you can rotate the image all day long without distorting it into some kind of spiral

>>11403319
>q=C*v * 120 per second so a person grabbing a 250k 60 hertz line would experience a current of 3mA
Is this fucking bait? For a capacitor, [math]
Cv'=i [/math] where v is the is the voltage *****over the terminals***** of the capacitor. The terminals of the capacitor are at the same voltage, so ******v=0***** and ******dv/dt=0****** which is a statement you already agreed with here >>11397425 and here >>11397786
So the capacitor *****has no current through it*****

>>11388974
What do i need to do in order to know as much math as the Yukari poster knows? :3

>>11388817
What kind of mental math should a person be capable of by age 30? I'm not 30 but I'm interested in this topic. Like what kind of math, and this is without scratch paper, should these ages be able to complete on the fly? Ages 5,10,15,20,25, and 30.