/sci/ - Science & Math

I want to impregnate patchouli.

Correct previous thread link: >>11863470

Unsansanswered questions:

Math questions:
>>11866503
>>11867063
>>11869582
>>11874488
>>11880575
>>11880590
>>11883337

Physics questions:
>>11867382 (It was answered but anon kinda depreciated his capacity to answer the question.)
>>11871097
>>11873718
>>11875247
>>11875651
>>11880246
>>11881016
>>11881341
>>11881430

Chemistry questions:
>>11885028

Biology and Medicine:
>>11864465
>>11868927

/g/ questions:
>>11864700
>>11867345 (This might actually just be maths, but he keeps writing FALSE in all caps so it goes here.)
>>11868197

Stupid questions:
>>11863795
>>11864977
>>11869588
>>11870393
>>11870440
>>11872091
>>11873433
>>11873980
>>11874321
>>11880745
>>11882343

>>11885812
Bro same.

I used to have a Patchy folder before my hard drive shit out, i havent been rebuilding it though
im sorry for letting you down bros

Try this, does your calculator max out at 2^33219 too or can it go higher?

>>11886124
>does your calculator max out at 2^33219 too or can it go higher?
LOL.
I do not use MS shitware so of course my calculator can go higher.

Imagine using a finite precision arithmetic calculator in the year of the lord 2020, it isn't the 60's anymore...

How long is it until gene modding becomes widely popular? And what are the limits of it?
I've watched a man on youtube cure, now reduce, his lactose intolerance by genetically modifying himself. Now, it's worn off after a few years.
But if you were to do something like that to height, what would happen? How do you even get started modifying your own body parts? I guess I'm looking for an answer on how to change myself, like becoming 6'7" extreme as an example, or other bodily changes. Hell if someone could even point me to an underground biohacking community I'd be grateful.

I'm trying to plot the black body spectrum of the Sun, but the graph I'm getting by using Planck's Law is two very narrow asymptotes near 0 with a value of 0 at x = 0. See pic related.
[eqn]L(x) = \frac{2hc^2}{\lambda^5 \left(e^{\frac{hc}{\lambda k_B T}}-1\right)}[/eqn]
This is the form of the law I'm using, which gives me the following by replacing the constants by their values:
[eqn]L(x)= \frac{2 \times 6.626 \times 10^{-34} \times \left( 2.998 \times 10^8 \right)^2}{x^5 \times \left(e^{\frac{6.626 \times 10^{-34} \times 2.998 \times 10^8}{x \times 1.381 \times 10^{-23} \times 5778}}-1\right)}[/eqn]
Which is input into the program like this:
L(x) = (2*6.626E-34*(2.998E8)^2)/(x^5*(e^((6.626E-34*2.998E8)/((x*1.381E-23*5778))-1))
Where did I mess up?

An ill posed question, out of curiosity

Denote by [math]\mathcal {F}[/math] the Fourier transform operator. Assume that [math]f, \hat{f}[/math] are both in [math]L^1[/math]. It is known that [math]\mathcal F \circ \mathcal F (f)(x) = f(-x)[/math] and that [math]\mathcal F \circ \mathcal F \circ \mathcal F \circ \mathcal F (f)(x) = f(x)[/math]. I'd like to think this is somehow related to the fact that [math]i^2 = -1[/math] and [math]i^4 = 1[/math], perhaps in a really trivial way. Maybe it's also related to the 4-periodicity of the derivatives of sine and cosine (i.e., differentiate each of them four times and you get the same function). Care to enlighten me please?

>>11885848
It's okay bro.
>>11887244
I'd sooner say that it happens because [math]\mathcal{F}(f)(x) = \mathcal{F} ^{-1} (f) (-x)[/math], which can be easily seen by comparing the two formulas.

>>11885028
try stirring it constantly, it sounds like you're getting a gradient and it's passivating the electrode.
Also sounds like an issue other people would have had, so look up their solutions

>>11886933
>Where did I mess up?
Firstly your brackets are fucked up.
L(x) = (2*6.626E-34*(2.998E8)^2)/(x^5*(e^((6.626E-34*2.998E8)/(x*1.381E-23*5778))-1))
is probably what you meant.
This is not the source of your troubles

Secondly. You are expecting a computer to calculate correctly. It does not. You should NEVER expect a calculation involving something like a 10^-34 or a 10^8^2 to give even a meaningful result unless you are *really* sure that the result will be correct.
Although this is also not the source of your troubles.

Thirdly. The expression is simply not defined for x=0, literally just a single look at the equation will tell you that.
What is the plot software supposed to do? It's probably shitty so it doesn't even give a warning to you, but it has to draw *something* so it draws some line to zero.
Here is the source of your troubles: NEVER trust a computer over common sense, it is very clear that the expression just is not defined for x=0, whatever the computer thinks about it can be safely ignored.

>>11885791
Going back to college after saving up money, taking up MATH 0001 (Pre-Calc 12) and PHYS 0312 (Physics 12)

anybody know any good books to prep myself for the 2 years I missed?

>>11886933
Your only issue is the scale you're working with. You aren't going to get a proper graph for that using a 1:1 grid.
Set your Y axis to go from 0 to [math]3 \times 10^{13}[/math] or thereabouts, adjust as needed.
Your X axis isn't in nanometers or microns, it's in meters. Set it to go from 0 to [math]5 \times 10^{-6}[/math].
>>11887412
You've got it completely wrong, besides pointing out the bracket thing.
He's looking for a black body spectrum, he's probably aware that 0 is undefined and puzzled about the peak in the negative X range because he didn't consider negative wavelengths would get plotted.

There's a normal distribution of speeds on a road. The average is 78km/h, top 5% is 90 km/h. What percentage is slower than 70 km/h?

First I find the normal distribution (90-78)/2=6km/h. Then I find the z-score (70-78)/6 = -1.333.... Then i look abs(z-score) up in normal distribution table = 0.9082 and use the normal distribution symmetry to find that it's (0.5-(0.9082-0.50))*100= _9.18%_ that drive 70 km/h or lower.

Am i correct? Cute cat photo for attention

>>11887465
If your goal is to be prepared for a course just look up the syllabus and start reading what you can of the actual course text

>>11887558
>top 5% is 90 km/h
What do you mean? The average of the top 5% is 90 km/h?

>>11887558
FWIW, I get σ=7.295, z=-1.0966, and 13.6%.

Find the z-score with a cumulative probability [-∞,x] of 0.95 (z=1.644854), divide 90-78=12 by that to get σ.

>>11887480
>You've got it completely wrong,
Oh fuck, yes. I totally missed the x in the exp, so the asymptotical behavior is actually towards zero, at zero...

Although I do believe that still every single one of my points stands:
2. Do not expect computers to calculate correctly.
3. Common sense > Whatever the computer says.

>>11887662
I assume he means 95th percentile, i.e. 5% of vehicles are travelling at or greater than 90 km/h.

>>11887272
>>11887244
I'm phone posting so apologies for the lack of latex but isn't this just because F is unitary? So taking the inverse is just the adjoint on L2. Well of course such notions don't exist in the standard L1 perspective but the formulas should work out the same.

>>11887671
>So taking the inverse is just the adjoint on L2.
Yes. The Kernel is [math]K( \xi , x) = \exp (- 2 i \pi \xi x)[/math], so that the kernel of the adjoint-that's-also-the-inverse is [math]K^* (\xi, x) = \overline{K(x, \xi)} = \exp ( 2 i \pi x \xi)[/math], that is, the sign on the exponent flips.
But the fact that [math]K(\xi , x) = K^* (- \xi, x)[/math] is specific to the Fourier transform, other unitary Kernels don't necessarily do it.

Is the poincare recurrence/quantum bounce idea legitimate and scientific?

What about the simulation/boltzmannian simulation argument?

why are blue eyes the only eye color mutation that have appeared in humans. does this lend credence to the yakub theory

What do we *mean* by 'negative voltage' and 'positive voltage'? Aren't electrons negatively charged regardless?

>>11888244
negative potential energy per unit charge, move a particle from a region of higher to lower electrical potential energy and you have negative potential difference.

>>11888217
>why are blue eyes the only eye color mutation that have appeared in humans.
How could they be if humans can also have green eyes and brown eyes.

>does this lend credence to the yakub theory
No. Nothing could lend credence to such absurdity.

this is a rigorous proof right bros?

>>11888261
brown eyes are not a mutation, and green eyes are just a melanated shade of blue

Are "data scientists" just glorified code monkeys?

>>11888300
Easier to say b=a+2, ab+1 = a(a+2)+1 = a^2+2a+1 = (a+1)^2.

>>11888449
that would imply they code
they're glorified excel monkeys

>>11888453
true

>>11888244
voltage is a potential difference. There's no absolute "potential" the only thing we consider is the change in potential from one point to another. this can go up or down, as indicated by negative or positive voltage

Which drug can I take to lower my sex drive

I'm stuck hard on this. I've found the 0th-2nd derivatives when evaluated at x=0 to be
[eqn] a + b + c = -2 [/eqn]
[eqn] -3a + 2 + 1 = 3 [/eqn]
[eqn] 9a + 4 + 8 = 4 [/eqn]

1st derivative:
https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(a%5Cleft(e%5E%7B-3x%7D%5Cright)%20%2B%20be%5E%7B2x%7D%2Bcxe%5E%7B2x%7D%5Cright)

2nd derivative:
https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdx%7D-3ae%5E%7B-3x%7D%2Bbe%5E%7B2x%7D%5Ccdot%20%202%2Bc%5Cleft(e%5E%7B2x%7D%2B2e%5E%7B2x%7Dx%5Cright)


Not sure what I'm doing, but wolfram alpha and this site other site both gave me saame answrs:
https://www.wolframalpha.com/input/?i=systems+of+equations+calculator&assumption=%7B%22F%22%2C+%22SolveSystemOf3EquationsCalculator%22%2C+%22equation1%22%7D+-%3E%22a%2Bb%2Bc%3D-2%22&assumption=%22FSelect%22+-%3E+%7B%7B%22SolveSystemOf3EquationsCalculator%22%7D%7D&assumption=%7B%22F%22%2C+%22SolveSystemOf3EquationsCalculator%22%2C+%22equation2%22%7D+-%3E%22-3a%2B2b%2Bc%3D3%22&assumption=%7B%22F%22%2C+%22SolveSystemOf3EquationsCalculator%22%2C+%22equation3%22%7D+-%3E%229a%2B4b%2B4c%3D4%22

https://matrixcalc.org/en/slu.html#solve-using-Gaussian-elimination%28%7B%7B1,1,1,-2%7D,%7B-3,2,1,3%7D,%7B9,4,4,4%7D%7D%29
So it has to be an error on how I'm approaching the problem, but I don't see what I could possibly be doing wrong.

>>11888901
SSRIs

>>11888905
I left out the b's and c's of the equations there for the 0th-2nd derivs but you get it

>>11888905
bro why are you using an equation solver for this. it's literally a 10 minute calculation if you do it by hand

>>11888921
I did it by hand as well, but it was much easier to show the work via links than tex

>>11888921
also, the equation solver removes any doubts I may have had about my arithemetic, so after my answers were getting denied I decided to check with that

>>11888961
if your hand answers suck ass and the equation solver agrees with you then the problem is wrong

>>11888905
> a + b + c = -2
That c shouldn't be there. Which is why you got the wrong answer.

Why do most lagrangians stop at the first derivative of q (they make the second one zero)? Is it because of newton's second law?
I remember seeing one up to the 2nd one, but forgot where, or if it has any applications

>>11889203
because the euler-lagrange equations don't consider the 2nd derivative. and also very few physical processes are dependent on the 2nd derivative

>>11889211
so, like an approximation?
nothing stops you from defining the varaition as [math]\Delta q=\delta q+\dot{q}\Delta+\frac{1}{2}\ddot{q}{\Delta t}^2+...[/math]

>>11889230
no? the euler-lagrange equation only considers 1st derivatives, because that's how it's defined.. I encourage you to read the derivation of Lagrangian mechanics to see why only 1st derivatives are considered.

how many processes can you think of that depend on the 2nd derivative?

>>11889235
But, you obtain the equations from the principle of least action, and you impose that the second derivative of q is zero, ok I get that.

But can you obtain one that considers higher derivatives anyways?

i've asked this before, but i'd like to verify one more time please, because i fear i might be missing something.

suppose [math]f: \mathbb R \to \mathbb C[/math] is continuous and of moderate decrease. suppose also that [math]\hat {f} = 0[/math]. claim: [math]f = 0[/math].
the hint given in the book is to apply the multiplication formula [math]\int_{-\infty}^{\infty} f \hat{g} = \int_{-\infty}^{\infty} \hat {f} g[/math], by choosing [math]g[/math] wisely. however my solution is as follows: both [math]f, \hat {f}[/math] are in [math]L^1[/math], so fourier inversion holds, therefore [math]f(x) = \int_{-\infty}^{\infty} \hat {f}(\omega) e^{2 \pi i x \omega} d\omega = \int_{-\infty}^{\infty} 0 d\omega = 0[/math] for all [math]x[/math], QED.

this one-liner seems way too easy and makes no use of the provided hint. does anyone see anything wrong with this argument?
perhaps this only shows that [math]f[/math] vanishes a.e., rather than everywhere? (i made no use of the fact that [math]f[/math] is continuous.)

>>11888307
>and green eyes are just a melanated shade of blue
So, in other words, a mutation.

>>11889259
>But can you obtain one that considers higher derivatives anyways?
The Euler Lagrange Equations are derived from considering first order integral functionals with linear constraints.

There is absolutely nothing in the Calculus of Variations which would prohibit you from writing down a second order Integral equation and although I know basically nothing about that case, I would assume that you, again, would arrive at something like an Euler Lagrange equation.

>>11889203
your question reads exactly like "why do we consider only the first derivative when we look for stationary points of a function f : R -> R"

>>11889425
>perhaps this only shows that [math]f[/math] vanishes a.e., rather than everywhere? (i made no use of the fact that [math]f[/math] is continuous.)
If [math]f[/math] is a.e. zero and [math]f[/math] is continuous then [math]f[/math] is constant zero.
Proof: Let [math]a[/math] be such that [math]f(a)>0[/math]. Then there's an [math]\epsilon [/math] such that [math]x \in [a - \epsilon , a + \epsilon ] [/math] implies that [math]f(x)>f(a)/2> 0[/math], so tje function isn't zero on a set with non zero measure.
If there's a problem, that's not it.

If I'm in a car moving forward at a speed of s and I throw a ball from the front of the car, I wanna find the speed of ball from outside observer, the equation would be x = s + b where x is the speed of the ball relative to the outside observer and b is speed of ball when I throw it, right? What is the equation if I throw ball from the side of the car?

Assume [math]f: \mathbb{R} \mapsto [0,\infty)[/math] is a continuous function and for all [math]\alpha \in [0,1][/math] , and [math]\sum_{k=1}^\infty f(k + \alpha) = \infty[/math]. Is it true that [math]\int_0^\infty f(x) dx = \infty[/math] ?

>>11890000
Set [math]f_k (t) : [0, 1] \rightarrow \mathbb{R}[/math] by [math]f_k(t) = f(k+t)[/math], for [math]k \in \mathbb{N}[/math].
Call the usual measure on [math]\mathbb{N}[/math] by [math]\lambda[/math].
Then [math]\int_{ \mathbb{R}} f ~ d \mu = \int _{[0, 1] \times \mathbb{N}} f_k ~ d ( \mu \times \lambda) = \int_{[0, 1]} \int _{ \mathbb{N}} f_k ~ d \lambda d \mu = \infty[/math], if [math]f \geq 0[/math], by Fubini.
I could be misusing Fubini, tho.

>>11890000
Don't think so.
Set [math]f(k + t) = f_k(t)[/math]. Define [math]f_k (t) [/math] for an integer [math]k[/math] by being constant one if [math]t \geq 1 -3/k[/math], then it goes in a straight line below to the point [math](1 - 2/k, a)[/math], where [math]a = 2 - k[/math], it then hops back up in a straight line to [math](1-1/k, 1)[/math] and stays at 1.
Since for every [math]\alpha[/math] there's a finite [math]k[/math] such that [math]\alpha \geq 1 - 3/k[/math], all the sums go to infinity, but the integral across each interval should zero (unless I fucked up the a choice).
It should work for nonnegative functions by Tonelli's theorem, tho.

>>11890122
*constant one if [math]t \leq 1 - 3/k[/math].
I've just noticed that the integral across the first interval doesn't zero, so I definitely fucked the a choice up. Ah, well, it's the principle of the thing.

>>11890122
Oh, and [math]k \geq 3[/math].

>>11889998
you have to think in 2 dimensions

>>11890122
>unless I fucked up the a choice
Yup, failed miserably. Teaches me to be cheeky and try to compute stuff with euclidean geometry while in a hurry.
Anyhow:
>bro trust me, the Riemann integral doesn't necessarily exist

>>11885791
wich 2hu would be the best mathematician?

>>11890122
>to the point (1−2/k,a)(1−2/k,a), where a=2−ka=2−k,
But that would mean that f(x) can be negative, right?

You say: "It should work for nonnegative functions by Tonelli's theorem, tho.", but the question clearly considers a nonnegative f...
What would the Tonelli argument be?

>>11890230
My bad, half blind.
Set [math]f_k(t) = f(k+t)[/math] for every integer [math]k \in \mathbb{Z}[/math]. Then [eqn]\int_{ 0}^{\infty} f ~ dx = \int_{ \mathbb{R}+} f ~ d \mu = \int _{ \mathbb{N} \times [0, 1]} f_k d (\mu \times \lambda) = \int_{[0, 1]} \int _{\mathbb{N}} f_k d \lambda d \mu = \infty[/eqn] , where [math]\lambda[/math] is the counting measure.
See the wikipedia page of Fubini's theorem for the statement of Tonelli's theorem. Counting measure and Lebesgue measure are clearly both sigma-finite, and if [math]f[/math] is continuous it's naturally measurable for the product measure.

>>11890257
I get what you are saying, but it feels a bit wrong to me. I mean, you could weaken the assumptions in the question to the sum being infinite on non-zero set of alphas.

(The measure/set products are the wrong way around in the third integral, right?)

>>11890294
>you could weaken the assumptions in the question to the sum being infinite on non-zero set of alphas
Non-zero measure, right? It's really only natural. Assume that the non-zero set is an interval or contains an interval, and you basically just get the original case back, except rescaled.
>(The measure/set products are the wrong way around in the third integral, right?)
Nope.

>>11890294
>>11890303
You know what, I'll just post a different proof:
Set [math]f_k(x) = \sum_{i=0}^{k} f(k+x)[/math]. Then, for any [math]K[/math], we have that the sequence [math]g_{k, K} (x) = \min (f_k (x), K)[/math] is dominated by constant K(integrable on the unit interval) and converges pointwise to [math]K[/math], so the Lebesgue dominated convergence theorem tells us that [math]\lim _{k \rightarrow \infty} \int _{[0, 1]} g_{k, K} d \mu = K[/math]. The rest follows by stacking inequalities.

>>11890303
>Nope.
So you really mean the counting measure over [0,1] and the Lebesgue measure over the Naturals?

>you basically just get the original case back, except rescaled.
I guess, but a slight difference is still there and this rescaling would not work in the negative case, I think...

>>11890329
* [math]f_k (x) = \sum_{i = 0} ^k f( i + x)[/math]

>>11890335
>So you really mean the counting measure over [0,1] and the Lebesgue measure over the Naturals?
No, anon, you invert the order of the measures when you do the d thingies. You have measure spaces [math]A[/math] and [math]B[/math], with measures [math]\mu _A[/math] and [math]\mu _B[/math]. Then you write down [math]\int_A [ \int _B d \mu _B] d \mu_A[/math].
Did this convention actually change?

why do things seem to better mix with water when it's hot?
e.g. you need to make jelly or puddings from powder with hot water, teas have more flavour when poured with hot water etc

>>11889998
>x = s + b where x is the speed of the ball relative to the outside observer and b is speed of ball when I throw it
Same thing but use the velocity vectors and then take the magnitude. Assuming the ball is thrown perpendicularly to the direction the car is moving, it'd be [math]x=\sqrt{s^2+b^2}[/math]

Thank goodness for these types of threads, needn't make a thread for just my own question. I'd like a way to plot two different numbers (y axis values) across distance (x axis) which have a linear relationship, and along the linear line I would like to be able to see what the value would be anywhere along the line. So in the picture for example, one point is at (200, 25), then the other at (900, 0). I would like to then be able to say, hover my mouse over the green line, or type in a x-axis value to see what the y-axis value would be. So for example, at x-axis 550, the y-axis value would be 12.5.

I've tried creating what I'm after in desmos, but I'm apparently too much of an idiot on how to do it. I know how to do this by hand/calculation, however I'd like a dynamic graph of sorts where I can change the variables (numbers) and quickly see anywhere along the line the number. I'm sure you can do this on desmos, if somebody could point me to the right direction or happens to know of a how-to guide so I can do it myself, that'd be great. If something doesn't make sense, feel free to ask.

>>11890681

>>11890681
You can just calculate the line crossing though the points. No idea about desmos, but if you just plot the corresponding function it should just work...

so is modern algebra basically just about exploring the concept of algebra itself? like instead of working in established structures you analyze and explore different ways of thinking about how numbers interact with each other?

>>11890796
Modern algebra is the study of algebraic structures, that is, it focuses on operations and the way they make a set behave, rather than the actual things that live in said set (not necessarily numbers, btw).

>>11890499
hot water has more capacity for dissolving things and has higher energy.
when you dissolve something, you break up the physical bonds keeping the atoms/molecules together. this is a physical process, and requires the water molecules to assist in breaking the intermolecular bonds. if the water has higher energy (moving faster) you can think of it having more destructive power.

>>11890713
I've created it and now have it saved on the website, thanks to your post, anon. Thank you.

What's going on in this vid? I can tell very small things are moving slowly over a period of days but that's all

>>11890828
how do you analyze operations? like, is it using logical axioms to confirm theorems and shit? how does set theory play into it?

>>11890888
>how do you analyze operations?
The same way you analyse anything, by asking question about what structures and regularities the thing inhibits.

>how does set theory play into it?
In standard mathematics every object is a set.

>>11890866
>l very small things are moving
How small?

My first guess is some sort of atmospheric re-entry. Perhaps camera onboard salleite recording its own demise.

Given the image quality I thought it may be produced with an electron microscope. Is this cellular?

>>11890888
It's done abstractly. One defines ideal properties for operations (e.g. associativity, commutativity, etc.); these will be the "axioms". Then we study the implications of having such properties.

>>11890888
>how does set theory play into it?
Most of the time is not used explicitly. The point of having the theory of sets is not having to worry about it higher areas of math.

>>11890000
Yes it is. If you want a full proof it will take some time to write properly but here is the idea:
For an M
you get a good subset of [math][0; 1][/math] such that the partial sum of its elements up to k are over M (strictly, it's astucious but mandatory). It exists for a big enough k.

Then you try to partition this set thanks to continuity so that [math] f [/math] doesn't vary too much on each translation of the partition (uniform continuity on the initial segment up to k). The goal is to find countably many open interval on which you can underestimate by a set value. which allows you to estimate the integral on [math][0; k][/math]. By taking a good partition and a big enough initial set (with measure nearing 1), you can underestimate the integral by [math]\frac{M-\epsilon}{2}[/math] thanks to the partial sums.

doable fo all M : the integral has no finite value.

>>11890257
Oh shit, didn't see this. Actually de-Fubinised the problem... your solution is much more elegant. Rather, you just need [math]f[/math] in yours (given that every projection is measurable), which is quite cool.

>>11890329
Actually this is exactly this proof but I re-prove some sort of domination's contrapositive... I feel bad when facing teh elegance of your proofs coupled with the cuteness of your pic...

I'm reading a book that has a set defined by comprehension like this:

[math]B = {n \in \mathbb{N}: -2 \leq n < 6}[/math]

and asks to define this set by extension, but it has the answer like this [math]B = {-2, -1, 0 ,1, 2, 3, 4, 5}[/math]

Isn't this fucking wrong? shouldn't it be [math]B = {0, 1, 2, 3, 4, 5}[/math] ? because it's natural numbers only.

(ignore the 0 if you don't think 0 is a natural number)

>>11891212
Yeah, they fucked up.

>>11891212
agreed they fucked up

(what fucking numbskull wouldn't consider 0 a natural number when doing math)

Does anyone know if there is a canonical wave equation with diffusion? Does anyone know of any papers with derivations? I've come up with a few equations that are what I want qualitatively, but I want to know if there is a definitive diffusing wave equation.

Here's an obvious candidate:
[math] \partial_{t\,t}f - \nabla^2(c^2\, f + \nu^2\, \partial_t f) = 0[/math]

Which comes from the time partial of the heat/diffusion equation with an added laplacian wave term. It visually exhibits the correct behaviors when simulated pic related. Its ugly thought with that partial of t inside the laplacian

>>11891440
Have you considered [math]\partial _{t ~ t}f - c^2 \Delta f + \nu ^2 \partial_t f = 0[/math]? On an intuitive level, if you ignore the laplacian term, you get [math]\partial_{t ~ t} f = - \partial_t f[/math], so we can "cancel the derivative out" to get [math]\partial _t f = - \nu ^2 f[/math], which is how I imagine (as a layman) diffusion works.

>>11891477
Nice double numbers. You know, although that equation isn't a conservation form, it has got me thinking. In absence of the wave term (as in when c goes to 0) the equation becomes the derivative of
[math]\partial_t f - \nu^2\,\nabla^2 f = k[/math]
Which also isn't a conservation form but I think it means that as long as the integral of the system over space remains constant in time that my original equation is conservative and likely really is the purest combination of the diffusion and wave equations. I just did a quick test and it looks good!

You got me out of a mental rut, thanks anon!

I need to find the solution to [math]t^2y(t)=H_a(t)[/math] using Laplace transforms.
After applying a transform I got a Cauchy-Euler equation with a solution [math]\mathcal{L}(y)=\frac{\alpha}{s}+\frac{\beta}{s^2}+\frac{e^{-as}}{s^2a}+\frac{1}{s}\int\frac{-e^{-as}}{s}ds[/math].
Is it possible to calculate the inverse Laplace transform for [math]\frac{1}{s}\int\frac{-e^{-as}}{s}ds[/math]? I thought about applying the convolution theorem but then I end up with an integral of an inverse transform of an integral.
Is the way I'm trying to solve the problem wrong?

>>11886601
Bumping for genemoding

Why do we split this up into two different [math] A_y[/math]? Why not just look at the interval [math]A_y = {x : r(x) \leq y} = {x : x^2 \leq y} \rightarrow [-\sqrt{y},\sqrt{y}] [/math]?

>>11892054
nvm am brainlet and went too hard on rote formula applying

Okay bros, how is it that I have curly hair even though my parents both have straight hair and it's a dominant trait?

>>11890329
Why would it be dominated by K? For each x, f_k tends to infinity.
>converges pointwise to K,
You mean to infinity?
I've no idea what you're talking about here. Perhaps you meant max(f_k(x), K)?

>>11892387
adoption

>>11892406
I'm not adopted though, I've seen the birth certificate

>>11892387
>>11892411
https://www.reddit.com/r/genetics/comments/c303ke/question_about_curly_haired_child_with_2_straight/

Currently planning on getting a math degree.
What should I do during/after to get a job in government/military? Any kind of job, really. Maybe some specific programming language?

>>11892874
>Maybe some specific programming language?
Absolutely. Programming is a top priority if you want to work outside of academia.
Other things you need to do: master proper voice technique (so you're able to speak well), business writing (so your writing is clear and succinct), persuasion skills.

>>11892905
>master proper voice technique (so you're able to speak well), business writing (so your writing is clear and succinct), persuasion skills.
Not that guy, but I'm extremely interested. Please bestow more advice to this little one.

Is it possible to have a spider infested house ("ecosystem") where the spiders only eat other spiders (because they already ate all the insects in and around the house)? How long can such an ecosystem go on in such a manner?

If someone who's momentum could be stopped by nothing but himself (like the juggernaut from the x-men, though it's not exactly the same) grabbed, say, a 1Kg ball of iron and just clapped their hands as hard as possible, crushing it into itself, would they cause nuclear fission? What would be the physical results of such event? Heat, gama rays, a blast wave?

What do you guys do in the first half hour of waking up?

I'm trying to have more productive mornings and notice a yuge correlation between my productivity and how slowly my day starts. If I spring out of bed, that momentum carries through the day, but if I lay there a little longer then groggle on out, that too carries throughout the day. It doesn't even really matter _when_ I wake up, it's _how_ I wake up (fast vs slow). I'd like to find a way to increase my motivation / enthusiasm for getting out of bed in this more snappy fashion, but nothing I've tried has worked and usually only makes me dread getting up even more.

The only things I'm able to do to help are just getting enough sleep and leaving some unfinished work for the next day. I'm hoping I can form a habit so this behavior sticks around, but I've had trouble going more than 2-3 days at a time at that pace before I crash and burn, Maybe it doesn't help that I set my own schedule.

>>11893851
I noticed that when I started snoozing my alarm it took me a lot more to get up. So now I wake up on my first alarm, shower immediately, then make breakfast and coffee.

>>11893945
Shower is a good idea to get the ball rolling. Sort of soothing and enticing as well so I won't dread it. I normally only shower at night but I'll try some AM showers, thanks anon

>>11893851
My experience is that the entire difference between waking up properly or not is cleaning up my tearducts with cold water.

do lights get brighter when you are moving toward them? and dimmer when you move away from them? from a relativity perspective of course. i know there is a change in light frequency but is there a change in light power too?

Does spacetime change at relativistic speed? From my understanding, you can never observe something going faster than the speed of light, but what about two near lightspeed objects traveling towards each other? What is the relative point?

>>11894225
lower frequency photons have lower energy, and the # of photons shouldn't change. So I'd say yes, moving away=lower power

>>11893710
yes

>>11894256
thank you

>>11893945
there's no harm in snoozing your alarm 15-20 times, just set it earlier. Comfiest way to greet the day if you're a slow riser

>>11894256
>>11894225
your response was wrong, energy!=brightness. the determining factor is photon flux per unit time, which is irrelevant of redshift

>>11894292
did you read the original post? if so you'd see how retarded this response is
>anon has correlation between productivity and starting the day faster
>lmao dude just start the day slowly!!!

>>11894261
So what would be the physical results of nuclear fission from 1Kg of iron?

>>11885791
I have a dataset of two column (x and y). They told me that this data set has a regression equation like \[ y = x^n \] and n is a real number beween 1.2 and 1.4. Is it possible to write an R or python script that helps me to find this n? Also, what is this kind of regression called? For it to be called an exponential regression, x should be the exponent, right?

>>11895028
Solve the exponential regression and use [math]x^n = e^{n ~ \log x}[/math]

>>11895037
Sorry for being a brainlet, but I'm not even into data science or any stem related career. How do I solve that equation? Or at least where can I find the documentation to do so?

>>11895058
Right.
You have [math] y = \exp ( n \log x)[/math]. We take logarithms of both sides to obtain [math]\log y = n \log x[/math].
So, to sum up: you define a new data set by taking logarithms of your old one, and then you use linear regression (with the constant equalling zero).

You can also directly compute the sum of the square errors to be [math]\sum_{j =1}^k (y_j - x_j ^n)^2 = \sum_{j=1}^k y_j^2 + x_j^{2n} - 2y_j x_j^n[/math] and the differential to be [math]\frac{d}{dn} \sum_{j=1}^k (y_j - x_j ^n)^2 = \sum_{j=1}^k 2 x_j^{2n} \log x_j - 2 y_j x_j^n \log x_j[/math], and then make your machine find a root.
Double check that computation btw.

>>11894838
since you do sweep through more photons per unit time does apparent radiative power of bright objects increase with speed? relativistic beaming im sure increases the apparent power in front of moving objects that certainly must entail observing higher power radiation from objects in front of you if you are moving

>>11895150
>since you do sweep through more photons per unit time
you don't though. if you did then the brightness would go up. all of this follows from the fact that the speed of light is the same in every single reference frame, meaning that if someone was traveling at 0.9c right at you and shined a flashlight pointing at you, you would view those photons as traveling at c. They're not boosted in speed

>>11895163
ah, yeah that is right. relativity is strange. i was thinking about the actual volume of space you pass through being greater per time when your speed increases but even that would be length contracted. so that approach should yield less photons too i think

I've hit a roadblock. I'm on the monotone subsequence theorem.
I'll lay the stage first.
Monotone Sequence Definition:
>A sequence is monotone if the sequence is either strictly increasing or strictly decreasing. Emphasis on the strictness.
Subsequence Definition:
>Suppose [math]x_n\in\mathbb{R}[/math]. Suppose [math]n_j[/math] is a strictly increasing sequence of positive integers (natural numbers). Then [math]x_{n_j}[/math] is a subsequence of [math]x_n[/math]
Monotone Subsequence Theorem
>All sequences of [math]\mathbb{R}[/math] have a monotone subsequence.
I believe I'm muddled on what it is exactly a subsequence is. Because if we consider the sequence [math]x_n=(-1)^n[/math] this does not have a monotone subsequence. We can take all the even [math]n[/math]'s but a sequence of 1s is not monotone. It does not strictly increase or decrease. I know but 1,-1 is a strictly decreasing sequence and -1,1 is a strictly increasing sequence, but then we have to restrict our subsequence here to be composed of two and only two elements of [math]x_n[/math]. Am I right in saying this cannot be a subsequence? Of course [math]n_j=j[/math] for [math]j\in\{1,2\}[/math]. But this is not all positive integers. So here are two questions I am posing.
>Is the definition of a subsequence silent on whether or not it can take all [math]n\in\mathbb{N}[/math] (i.e. it is entirely possible a subsequence can be finite)?
>Am I correct in saying [math]x_n=(-1)^n[/math] has no monotone subsequence, with the stage set?

>>11895028
Use scipy.optimize.curve_fit

>>11893851
I jerk off, eat breakfast, play starcraft and then do math. It doesn't matter how slowly my day starts.

How do I, as a midwit, cope with it? I can't get into STEM and do well or ever learn all the fun things I've wanted to learn and be proficient at.

How have you other midwits coped?

>>11895315
Just lie down and die.

>>11895327
I've been just lying down. Haven't died yet.

>>11895315
im sorry to say anon, but if you cant get into stem then midwit isnt the appropriate term

>>11895286
Either the strictness part is incorrect (in which case you have the usual statement of the theorem) or the sequence isn't allowed to achieve the same value twice.
>>Is the definition of a subsequence silent on whether or not it can take all n∈N (i.e. it is entirely possible a subsequence can be finite)?
Allowing finite subsequences just trivializes everything.

>>11895351
I'm not going to attempt to spend money on something I will fail at. I could become HR and instead of hiring high iq's who were born lucky with good genes diversity higher instead.

>>11895354
I thought as much. Many thanks

>>11895354
>>11895373
BTW, I just thought of this in the shower, but the correct statement is that it has a strictly decreasing/increasing subsequence if and only if it achieves infinitely many different values.
Proof reader left. It's very short. If you start doing something long, it's incorrect.
Hint 2: use the version from earlier.

>>11895310
i do the same (dia toss player no big deal) but probably just have more I need to get done on a monthly basis then you

>>11895388
I... I'm just stupid. I set the stage wrong and completely fucked myself. A monotone sequence is not strictly increasing or decreasing. It is just increasing or decreasing. At least that is the definition we are using. It is entirely possible a constant sequence is monotone.

All these problems with first and second fundamental theory of calculus. I see the integral symbol, I go up. I see the derivative symbol, I go down. What the fuck am I supposed to be getting besides that they're inverse operations of each other? Me crunch number, and it's just a black box in between. I don't understand why my definite integrals between some constant (a) and x of some function of some variable need to be represented by some other capital letter (not f!) and with independent variable x instead of whatever independent variable the integrand had. Why can't they just tell us F(x)=integral of f(x) and leave it at that.

>>11895332
Then die. Retard.

>>11895669
stop rambling and ask a coherent question if you don't understand it

>>11895703
please don’t help retarded people. If you can’t understand the fundamental theorem of calculus you deserve to fail out of university.

>>11895703
What more is there to understand from the first and second FTC besides integrals and derivatives being inverses of each other? Anything critical that would prevent me from continuing to perform calculus as a non-math major?
>>11895708
Get the fuck out of this thread if that's your attitude.

>>11895719
what exactly are you having a hard time understanding? is your question that you just don't understand them?
the first FTC is that derivatives and antiderivatives are opposites, and the second relates the integral to the antiderivative. both of them together say that integration is essentially the inverse operation of differentiation.

it's like the fundamental theorem of algebra, it's not inherently interesting unless you're a math person. but you use its applications all the time, you just aren't going "I'm now invoking the first fundamental theorem of calculus" you just integrate the thing
I recommend looking at the proof on the wikipedia page because it's really easy to understand and helps you see why it's not a "black box" operation

>>11895719
>non-math major
Seems like you understand everything about FTC for your needs. But if you are bothered by the black box, take an intro to analysis course. Who knows, you might join the dark side and end up being a mathfag.

>>11885791
Scientifically speaking, why do anime legs make me rock hard and want to breed these fictional drawings? More so than any photo of a real woman.

>>11895744
mental illness, lack of human interaction

>>11895744
theyre more attractive by design

>>11894838
>determining factor is photon flux per unit time
I thought it was power density

>>11895836
that's if you're considering fields as opposed to photons. however then in order to find the total brightness in a boosted frame you have to transform the power which is a more roundabout way at arriving at the same answer.
the question ultimately boils down to "does changing the energy of light change its brightness" to which the answer is no. it's merely the intensity that changes.
also this just reminded me how much the units/science surrounding this topic is fucked. the wikipedia page for "radiant energy" has like 50 different SI units all describing different things

>>11885791
Did we figure out if the universe is flat or not? A quick google search had conflicting answers, and I doubt I can really be sure from first page results from google. Any good reads, for a layman?

>>11895918
no we haven't

>>11895923
Hey hey I know you and I haven't figured it out..yet.

>>11895929
I'm not working on this problem, thank god. it seems hard to test

>>11895719
you are a brainlet, you will always be a brainlet. this was written into every cell, every tissue and organ of your body at conceptions. this was decided centuries before your birth. you cannot escape this.

>>11895944
Neji thought the same thing but got his ass beat by Naruto.

>>11895946
Naruto is for normalfags and the mentally retarded. If you didn't watch Yu Yu Hakusho as a child you're not going to make it

>>11895955
I like both but the rarity of someone acknowledging Yu Yu Hakusho makes you an absolutely based poster.

>>11895127
I have a bit of an even more brainlet question. Let's say the equation isn't really [eqn]y = x^n[/eqn] but [eqn]y = x^n + 21[/eqn]. My dataset has the values of x and y, from x=1 to x=200 (y is 21 on x=1 btw). What I tried to do was to create a new dataset in which y=x^n by subtracting 21 from the y column. The curve should have the same shape but staring on y=0 instead of 21, so I can apply the method you proposed (after removing the first row because ln(0) is -inf), and get to a valid answer. Are my assumptions correct? Or am I missing something? What would be the right way to solve it then?
I ask because, with the actual equation, [math]ln(y)[/math] would no longer be [math]ln(e^(n*ln(x) ))[/math] which can be simplified to [math]n*ln(x)[/math], but instead it'd be [math]ln(e^(n*ln(x)) + 21)[/math]

Can someone explain why the inverse mapping of [math]f:[0,1)\rightarrow S_1[/math] is not continuous?

>>11896276
Oh and the mapping is [math]f(x)\mapsto (cos(2\pi x), sin(2\pi x))[/math]

>>11896276
the image of [0,1/2) is not open

>>11896285
I know that, but I want to know why it isn't open.

>>11896294
the point (-1,0) in S^1 doesn't have an open neighborhood lying in f( [0,1/2) )

>>11895719
FTC says that if f is continuous on [a,b], then

f(x) = lim h->0 F(x+h)-F(x) / h

where F(x) = the supremum of lower Riemann sums of f on [a,x] over all partitions of [a,x]

nothing more, nothing less.

>>11895744
Because they are created specifically to evoke that emotion in you.

>>11895669
> I don't understand why my definite integrals between some constant (a) and x of some function of some variable need to be represented by some other capital letter (not f!) and with independent variable x instead of whatever independent variable the integrand had.
You mean why do we write down [math]F(x) = \int_a ^x f(t) ~ dt[/math] rather than [math]F(x) = \int_a^x f(x) ~ dx[/math]?
That's essentially because, from the moment you pick an [math]x[/math] (that is, attempt to evaluate the left side), [math]x[/math] becomes a constant, and you can't integrate along constants.

Is there a symbol for the set of all scalars?

>>11896726
[math]\mathbb{K}[/math] is used often enough to "denote either [math]\mathbb{C}[/math] or [math]\mathbb{R}[/math]"

>>11896750
danke

Why is high or even infinite impedance desirable for voltage-controlled devices like op-amps and FETs? I understand it reduces power consumption, but how can voltage be amplified across a high impedance? Wouldn't that just result in a voltage drop?

>>11896750
Literally nobody ever uses it. They do use [math]k[/math] though.

>>11896793
>Literally nobody ever uses it.
Way to show off your lack of studying.
>They do use k though.
They use [math]k[/math] to denote an arbitrary field, that's different.

>>11896793
>Literally nobody ever uses it.
literally everybody use it you fucking undergrad

>>11896834
>>11896815
Show one (1) example.

>>11896836

>>11896839
Must be a book for retards, that one. Give three (3) more examples.

>>11896842
Bro I'm not spending half an hour looking through my .pdfs for more examples, go fuck yourself.

>>11896845
>go fuck yourself.
Already did two times today.

>>11896842
not that anon and this is literally the book I'm reading right now, I didn't even have to look. enjoy being a brainlet.

>>11896854
hmm I'm just going to ignore this because it contradicts my opinion

>>11896839
based
>>11896842
cope

>>11896793
literally the anon you cite just used it

>>11896842

>>11896854
>>11896871
I meant literally either [math]\mathbb{C}{/math] or [math]\mathbb{R}{/math]. You aren't going to find examples in algebra, but there's some stuff in analysis that literally only works for these two, and sometimes also the quaternions.
Say, Banach spaces and Hilbert spaces are only really relevant over those two fields.

>{/math]

>>11896793
It's standard faire in functional analysis and Lie theory, where the latter includes the quaternions as well.

>>11896854
>characteristic != 2
can we all just agree that fields with characteristic 2 are the niggers of fields?

>>11896761
A high input impedance avoids affecting the preceding stage. A voltage-controlled device doesn't need to draw current to work, so the less current it draws the better. The impedance has nothing to do with the amplification.

Is the function [eqn] f(x) = \frac{x}{x} [/eqn] defined at [math]x=0[/math]?
Of course its limiting value as [math]x\to 0[/math] is 1, but then is it okay to actually then say that [math]f(0) = 1[/math] even though that requires division by 0?

>>11897232
it's technically not defined at x = 0, but since it has a limiting value it's a removable, discontinuity, literally just a hole punched out of the graph of the function
so it's no big deal to just redefine it as the limiting value at x = 0

>>11897243
Thanks mang

>>11897194
Yes.
I do get the impression that the result that all vector spaces have bases is particularly important for [math]F_2[/math] tho.

what are some good sources of information about more advanced ML stuff like CNN, RNN and etc.? i thought towards data science/medium was decent but every article i've found about RNN on them was written in broken english by pajeets

Is the accuracy of weather prediction only constrained by a lack of data or are the models themselves incomplete? Say there was a weather station every tenth mile, would the forecasts be pretty much perfect?

If I place a charged body next to a neutral conductor, will the conductor be attracted to the charged body?
>put negative charge next to neutral conductor
>electrons in conductor repelled by negative charge
>side of conductor far from charge is negative
>side of conductor near charge is positive
>negative charge attracts near positive charge more than it repels far negative charge
>conductor moves toward charge
>start over with positive charge
>...
>still attraction?

>>11898232
weather is unpredictable. there are so many factors that go into it that no matter what it'll never be perfect

>>11898281
yes

>>11898281
Yes, look up "Induced Dipoles"

>>11898232
The system is chaotic, so even the smallest error will eventually completely change the result. More accurate data would make the short-term forecast more accurate and push the point where the forecast becomes too unreliable to be useful farther into the future. It would probably also allow the models to be improved a bit.

[math]D[/math] is a subset of [math]\mathbb{R}[/math] and [math]f : D \to [-4, + \infty) / f(x) = x^2-4[/math] so [math]f[/math] is bijective if [math]D = [0, + \infty[/math]

how do you prove that it is bijective by [math]D = [0, + \infty[/math] ?

>>11898755
Define the inverse by [math]g : [-4, \infty) \rightarrow [0, \infty)[/math], [math]g(x) = + \sqrt{x + 4}[/math].
Das it.

if i have a function f : A -> B, is it always true that cardinality of A is ≥ cardinality of f(A)?
seems intuitively true to me but I don't want to make any half assed assumptions

What’s the truth behind covid-19? /pol/ is split between believing the virus doesn’t exist and claiming that it’s airborne Lyme disease/AIDS. Now there’s a study saying there’s no long term immunity, but it hasn’t been peer reviewed and I’ve read there were other studies that found T cell immunity was robust. What does the data and science show?

>>11898781
If there is a surjective map from A to B then card(A) >= card(B). Obviously the map f is surjective onto its own image so yes, the inequality holds.

>>11898781
It should be evident from the definition of image of a function.

>>11898801
>>11898803
ok thanks, just wanted to make sure
always struggled with basic set theory results, maybe I should brush up for my own sake

How would I show that in a module M of finite length with an endomorphism f, it is possible to find a natural number n s.t. [math] M = \text{Ker}f^{n} \oplus \text{Im}f^{n} [/math]?

I know a finite length module is both artinian/noetherian, and obviously I imagine that if I just take the sequences [math]f(M) \supset f^{2}(M) \supset ... [/math] and [math]\text{Ker}(M) \subset \text{Ker}^{2}(M) \subset ... [/math], I'll find an n where the images and kernels become constant even if I keep composing f with itself for longer. Eventually this lead me to believe that [math] f^{n}[/math] could be idempotent, cause then if I composed it with itself obviously both the kernel and the image would stay the same, and that would have helped because I also found https://math.stackexchange.com/questions/566685/a-module-as-an-external-direct-product-of-the-kernel-and-image-of-an-idempotent . But the problem is that even if it was true, I don't think that showing that the sequence of kernels/images is constant is enough to prove the morphism has to be idempotent (like how any 2 automorphisms have the same kernel/image but the composition doesn't have to be equal to either of them). Anyone has an idea how I should move forward?

>>11898766
what if you don't know that [math]f[/math] is bijective if [math]D=[0, +\infty) [/math] and have these other 3 options:

1) [math]f[/math] is injective if [math]D = [-2, 2][/math]

2) [math]f[/math] is surjective if [math]D = [2, + \ifty) [/math]

3) [math]f[/math] is bijective if [math]D = \mathbb{R}[/math]

? you have to check one by one?

>>11898841
Those are all very easily false:
1) D = [-2, 2] contains -2 and 2, which have the same image, so it's not injective.
2) If D = [2, infty) then -4 isn't in the image, so it's not surjective.
3) If D = R, then it again contains -2 and 2, so it's still not injective.

>>11886313
Why in the flying fuck would you need a calculator that can go higher than that?

>>11898791
science doesn't move arbitrarily fast. high-quality research on this will take time.
that being said /pol/ is retarded, the virus absolutely exists and you should stop visiting that godforsaken board

t. work in a hospital

>>11898899
>you should stop visiting that godforsaken board
t. sci user

>>11898908
/sci/ has a few good threads once you filter all the IQ, race baiting, and conspiracy threads. So basically when you filter out /pol/ and /x/ influences.

>>11885791
Can someone please explain the difference between pointwise convergence and uniform convergence for sequences of functions?
I don't understand why putting the [math]x \in A \subseteq \mathbb{R}[/math] before in the statement changes everything

>>11898933
Let [math]\epsilon>0.[/math] For pointwise convergence, the [math]\delta[/math] that you find will depend on [math]\epsilon[/math] and the point [math]x[/math]. For uniform convergence, the [math]\delta[/math] you find will only depend on [math]\epsilon[/math].

>>11898951
Yes, I get the idea, but why does one definition imply a different thing from the other?

>>11898961
one textbook I used talked about an "epsilon sleeve" around the function for uniform convergence (see pic I made in Desmos), whereas you don't get such a thing for regular pointwise convergence

thinking of the convergence of x^n to f = 1 on (0,1] not being uniform also helps me

>>11898933
Pointwise convergence is pretty straightforward, the name says exactly what's going on: each point of the function converges to the limit function, and that's about it. You don't know much about how fast each point converges, maybe some points approach the limit really quickly while others not so much, and when you are talking about an infinite amount of points (usually even uncountably so) it isn't really possible to bound the function as a whole.
Uniform convergence is what you require in this cases, like >>11898951 says just putting the [math]x \in A \subseteq \mathbb{R}[/math] before the statement means that the existence of [math]\vardelta[/math] does not depend on x anymore. Basically not only does each point converge individually towards their respective limit in the limit function, but every single point converges at a similar rate, so to speak.

As for the statement itself, there's a difference between saying "for every x there exists y" and "y exists (such that) for every x". The latter implies that whatever y is, it's specific to whichever value of x you take, while the former means there is (at least) one y that lets a property hold for every value of x.

>>11898967
Also I guess I really need to brush up on tex, but hopefully you still get the idea

>>11898966
meant to say x^n converging to f = 0 on [0,1)

Here's how I understand Dirac delta.
>Start with a 1x1 square, bottom edge on the x axis, centered on the y axis
>Grind off some of each side
>Lay the dust on the y axis above square
>Grind some more
>Extend the line of dust
>The shape gets thinner just as fast as it gets taller
>If you grind infinitely fine dust you get an infinitely tall line
>The total area of the shape is still 1
I suppose lim(x->infin) (x * 1/x) = 1.
The problem is I now realize this line of reasoning assumes from the start that the shape has area 1.
If I started with a rectangle that was twice as wide as the original square, the final shape would have an area of 2, but it would be described by the same rule: y = infin when x = 0 and y = 0 everywhere else.
With that in mind, how should I understand that the area of the Dirac delta is 1?

>>11899022
start with the normal distribution (of integral one)
[math]lim_{\epsilon \rightarrow 0^+} \frac{1}{\sqrt{2\pi \epsilon}} e^{\frac{-x^2}{2\epsilon}}[/math]
The integral should still be one since you maintain normalization but in the limit you obtain the delta function. Proving that the function I gave you is equivalent to the delta function is a different matter.

>>11899022
From what I understand, physicists are more open to accepting such an object like the Dirac delta, and that kind of derivation is the sort of reasoning they use. Mathematicians don't like it because it's not rigorous, and your example shows one of the many possible things that can go wrong.

If you really want a rigorous definition of the Dirac delta, you need measure theory or distribution theory. Then the Dirac delta would either be a measure or a distribution.

>>11899022
part of the problem is that the delta function needs an integral of one by construction, it's not that this value just "pops out" when you integrate it. you could just as easily define its integral to be 69

>>11899022
>how should I understand that the area of the Dirac delta is 1?
Honestly you shouldn't, it's more likely to do more harm than good. Dirac delta isn't even a "usual" function but a distribution so trying to force the intuition of area under the function's graph isn't really something you can apply here. Also, under that intuition you could get the area of the integral to be whatever you want (just pick an area A and start with a [math] \sqrt{A} \times \sqrt{A}[/math] square). Lastly, you may come into trouble if you try evaluating the integral of [math]2 \delta[/math] or just some other constant in general, because they intuitively have the "same graph" but the "area" changes.

>>11899055
what exactly is a distribution?

>>11899078
an array of numbers

>>11899078
a linear functional on an appropriate function space, a probability measure, etc

Can anyone help me solve the n hats/n people problem using Burnside's lemma? The problems goes as follow:

n people wearing n indistinguishable hats go to a party and leave their hats at the door. Upon leaving, each guest picks a hat at random. Prove that, on average, only one of the guests gets their own hat back.

Now, I have no idea what to do here. I guess it has something to do with the group action of [math] S_n [/math] onto [math] \{ 1,2, ...,n\} [/math] when fixing one point but I don't even know what "on average" means. Any insight would be appreciated.

>>11899124
Turns out I didn't understand Burnside's Lemma at all. Once I did, it was trivial. In case anyone is wondering:
Let [math]X[/math] be the set of hats. Since they're grabbed at random, every permutation can happen. In particular, if [math] x,y \in X [/math] then there is some [math] \sigma \in S_X [/math] such that [math] \sigma (x) = y [/math]. Therefore, the action of [math] S_X [/math] on [math] X[/math] is transitive, so it has only 1 orbit. By Burnside's Lemma: [eqn] \frac{1}{ | S_X | } \sum_{ \sigma \in S_X } X^{ \sigma } = 1 [/eqn]. Therefore, the amount of fixed points on each [math] X^{ \sigma } [/math] or, to put it another way, only 1 guest gets his hat back "on average".

For the autist that creates these threads, this is from Based 't Hooft himself:

http://math.ucr.edu/home/baez/physics/Administrivia/booklist.html

A curated physics textbook list with comments from actual physicists. You should consider adding this to the template for the new threads.

Love,

Anon

>>11898967
This helped thanks

>>11898966
This helped as well, thanks

how accurate are paternity tests?
say you don't reveal any information to the doctor that you have a twin and/or from a multibirth and have more than 10+ brothers from the same two parents, many more half bros from only the father's side and some from your mother. Add that you have many male nephews, male cousins, uncles, and your 4 grannies had big families too.


Without telling the doctor are the results of the paternity test to be trusted?
What if there's proof she's fcuked the entire family? what if there's none or the woman didn't?
Some sources say they're 100% absolutely accurate and the only room for error is ill-intent. We all know the same thing's been said about fingerprints being 100% too but time revealed they're unreliable and fingerprints/dna aren't truly unique.

>>11899022
It's straightforward if you use the definition of delta as a limit of a higher-order function:

[eqn]\delta_\tau(x)=
\begin{cases}
{1 \over \tau} & 0 \leq x \lt \tau \\
0 & \text {otherwise}
\end{cases}
\\
\delta = \lim \limits_{\tau \to 0} \delta_\tau
[/eqn]

>>11899705
This is not true at all

>>11898840
Anyone?

>>11898840
>Anyone has an idea how I should move forward?
[math]n[/math] is large enough for the image and the kernel to stabilize.
Assume that [math]ker ~ f^n \cap im ~ f^n \neq \emptyset[/math]. Then, there's some [math]a \in ker ~ f^n \cap im ~ f^n[/math]. So [math]a = f^n (b)[/math], for some [math]b \in M[/math]. But [math]b \notin ker ~ f^n[/math] and [math]b \in ker ~ f^{2n}[/math], violating the earlier hypothesis that n is large enough. Thus, those two have empty intersection.
What all of this implies is that [math]f^n |_{Im ~ f^n}[/math] is injective. Because [math]im ~ f^n = im ~ f^{2n} = f^n (im ~ f^n)[/math], the restriction is also surjective.
Denoting by [math]g[/math] the inverse of [math]f^n : Im ~ f^n \rightarrow Im ~ f^n[/math], we have that, for any [math]a \in M[/math], [math]a = (a - g(f^n (a)) + g(f^n(a))[/math], the desired decomposition.
>>11899330
Very nice.

>>11899837
My bad, it's not empty intersection, it's [math]\{ 0 \}[/math]
And the [math]a[/math] is non-zero.

>>11899022
>Here's how I understand Dirac delta.
Either pretend that it does exactly what it should do and don't think about it, or do it rigorously via measure theory.

Trying to understand something rigorously, which *can not* be explained rigorously in your framework will only confuse you, as it will never make any sense.

>With that in mind, how should I understand that the area of the Dirac delta is 1?
You have to understand it as a measure. Or, more general, as a distribution, then it will make sense.
The issue is that from the "intuitive approach" it is very unclear why the integral should be 1 and not 1.01, for example.

>>11899705
>lim
Yeah, if you know what "lim" means in this context then you already know very rigorously what the dirac distribution is.

I can't understand how to interpret this graph, which should represent the cross section in the scattering of alpha particles on gold (the Rutherford experiment). The blue curve represents the calculated cross section for the nuclear Rutherford model, while the black one represents the uniform sphere Thompson model. What I don't understand is why the black one isn't a function: I expect the values to drop to 0 after 10^-3 radians because in the Thompson model the particles can't be scattered at large angles, but instead it turns back in a way that doesn't make any sense to me. Am I a brainlet or is the graph wrong? Anyone has an explanation? Thanks a lot.

>>11886124
mine goes to 2^1783446565

>>11898853
Because it is a full computer algebra system. There is LITERALLY no reason to calculate in finite precision integer arithmetic in the year of your Lord 2020.
Maybe in the 60s you could justify that, but even in the 70s that was outdated...

with neural networks, if my test accuracy caps at 80% but training accuracy goes up to 90%+ with more epochs (test acc stays more or less the same), i should try to make the network a bit more complex (to go beyond 80% on test) but reduce the amount of training to not overfit, right?
i know the theory but i really suck at practice in ML

I'm not sure if I understand this correctly, but if our hypothesis predicts 1, and our model is 0, doesn't the second term make our cost log(0)?

>>11900103
The cause can be any number of things.
By the way, nobody knows what you should do. Just try and see if it works based on your intuition.

But I don't think your plan is too bad, but you should also really consider switching up your network architecture.
Also, there is absolutely no reason to "train less" unless you legitimately see a drop in accuracy...

>but i really suck at practice in ML
It's literally gut feeling.

>>11900223
the prediction (h) is the result of sigmoid function in this example, so h is between 0 and 1, not either 0 or 1
NN output is (almost) always a floating point and in this case of classification it's up to you to decide whether the result should be 1 or 0, you can sorta interpret h(x) as a probability of result being 1

>>11900287
the samples we're given in the problem make it effectively 1 or 0, if it's not log(0) by computation, then it's a very large number to make it effectively infinity. That's what I don't get about this cost function during initialization, if h = 0 and y = 1 then the first term goes to +inf, and if h = 1 and y = 0 then the second term goes to +inf

>>11885791
What are some interesting/entertaining, active, astronomy-based YT channels? The only one I know of isn't really active anymore.

>>11899078
Just a fancy word for a functional on a vector space, typically an infinite dimensional one. In other words, an element of its dual space.
For example delta is usually thought of as an element of S*, where S is Schwarz space.

>>11900384
if h ~ 0 and y = 1, then the first term makes the error huge (as it should be), if h ~ 1 and y = 0, then the second term makes the error huge (as it should be) so you're correct
if the fact that it goes to infinity is your problem, keep in mind that everything is computed on computers, not on paper, so log(~0) is in reality just a huge number (how big depends on low level implementation) , not +inf (and the number should be that huge if the error is that drastic)

How do you realize that a function is continuous by just looking at a graph? if there's no cut in the line?

>>11900441
this is a hand-written problem which is why I was asking, your answer clears it up.

>>11900469
Sure. You just make sure it approaches the function value at every point from both sides of the point.

>>11900469
if there exists any point on the curve where a point isn't defined it's not continuous.

>>11900469
>if there's no cut in the line?
It helps in many cases, but not always. The main point of having a formal definition of continuity is crushing that intuitive reasoning. Check, for example, Thomae's function (pic related), which is continuous at all irrationals even though has a lot of cuts.

>>11899837
Thank you, that's even more detailed than what I expected so it really helps

it's easy to find lots of geometric/topologic properties that make the moebius strip stand out as a surface (like non-orientability, just having one edge, etc), but does anyone know of a book or just a text in general that actually proves these formally?
the geometric intuition for most of these is really easy to understand just by looking at it, but i want to know how they are actually proven

are there any scientific ways to reduce stress? I've heard reading for 20 minutes per day does

>>11900469
>How do you realize that a function is continuous by just looking at a graph?
You can not in general do that.

In 99.9% of the cases the argument is that a function is a composition of continuous functions.
If that doesn't work you will have to do legwork...

Really having trouble seeing why this isn't just 0

[eqn] \displaystyle \lim_{(x,y) \to (-3,-3)} \frac{e^{x^{4}}-e^{-y^{4}}}{x+y} =????[/eqn]


The question said 'use continuity to evaluate the limit'

>>11900798
>why isn't it just zero
Because [math]\exp (81) - \exp (-81) \neq 0[/math].
>>11900573
> but does anyone know of a book or just a text in general that actually proves these formally?
Maybe a book on topology of surfaces.
But proving that the Mobius strip isn't orientable is a huge pain in the ass, I doubt you'll find that anywhere.
Outline as follows: define the orientation bundle, show that it's connected.

>>11900826
1.50609731463e35 isn't an accept answer either

>>11900858
You forgot to divide it by -6.

why does my network get worse in both training and testing sets with more epochs

>>11901004
Only marginally?
It can be the case that the optimizer has found a pretty good local maximum for the network and now will, at the start of each epoch, try to aggressively leave that local max, but the network doesn't really permit anything better.

Try adding more layer, changing the activation function, do pooling/dropping, etc., etc. and see what works best.

>>11900798
>use continuity to evaluate the limit'
Since this is a composition of continuous functions, at least in a neighborhood of (-3,-3) this mean you can just plug in the values as if there was no limit.

halp pls

>>11901169
do you know what the symbols mean

>>11901185
yeah i figured iit out now

>>11901113
it goes down by quite a big margin, e.g. accuracy in training set gets up to 0.77 in the first epoch, then the second is 0.75, and third 0.66

Is there some way to see that there exist no other 1-dimensional "spaces" besides infinite lines, line segments, and circles? Maybe I'm being technically imprecise but I think you know what I'm getting at.

Is the reflexivity of the = symbol (i.e. x = x) really necessary for mathematical proofs? What happens if we abandon this condition?

What exactly is the euclidean (if it can be called that) or 2-norm of a matrix? I know how to compute it, but what does it represent geometrically? Like the way the euclidean norm of a vector in R2 represents the length of that vector.

>>11901353
by 2-norm do you mean treating an n x m matrix as a vector of length n*m and taking the euclidean norm of that vector?

>>11901353
The length of the vector. Draw a vector in the plane on a piece of paper, decompose the vector component-wise. Now use trig to convince yourself the norm is precisely the length of the vector.
>>11901378
The 2-norm (L-2 norm) is rbe norm induced by the standard inner product that one uses when you take the square root of the sum of the squares of a vectors components. He’s just referring to it in a funny way.

>>11901330
Then there exists at least an element k in whatever space you are working with such that [math]k \neq k[/math], or [math]k-k \neq 0[/math], and the entire algebraic structure of any set that requires an additive identity element gets immediately fucked.
Even if it is a non-algebraic set, what would = even mean anymore if it is not reflexive? An element not being equal to itself pretty much invalidates the whole purpose of defining =, even if your calculations are correct, if you get to an equation and find a value for a variable (say, k = f(x) or something) then what would it mean to have solved the equation? Sure, now you know k is related to f(x) under =, but that still wouldn't allow you to say they are the same element, because no reflexivity means that it is possible for the relation to be true even if they are different values, which for = in particular is very bad.

>>11901330
then what does anything mean? you have to make some claims and definitions as the basis of math

do i get that correctly that RNN layer is actually a single neuron and when setting the output size in e.g. keras, it's just how many "loops" the RNN does?

I have a question about multivariable functions.So, a function of two variables, for example, is a function in which there are two variable arguments, and one of those arguments happens to be a function of the other ( y is a function of x). A function of three variables, is a function with three variable terms, and one argument is a function of another, which itself is a function of the last term (z is a function of y which is a function of x). It would seem that, in order for a multivariable function to exist, each of it's arguments must be related. This might be a stupid question that I could resolve on my own with a little bit thought, but why? Why won't unrelated variable arguments work? Also, please clarify for me how this is different from compositing functions. Sorry for the stupid question but that is what this thread is for.

>>11901425
>one of those arguments happens to be a function of the other
That does not need to be the case in general, the variables don't need to be related at all.

When the variables are related, you're usually imposing some sort of extra conditions, as is often the case in optimization problems for multivariable calc

>>11901207
How long is the training? If it's minutes per epoch just let it sit for a while and see if it goes back up after some time, it can just be some local max.
Otherwise I would seriously consider adapting the network...

>>11901440
So, rather than looking at it like "z is a function of y which is a function of x", I should instead treat them as "a(x), b(x), and c(x), so to speak? Unrelated changing values?

>>11901353
>but what does it represent geometrically?
Imagine the unit ball around zero. Any matrix will map that unit ball to an ovaloid, the shape of the ovaloid is directly connected to the singular values of the matrix, the largest singular value being it's norm.
The largest distance from 0 to the boundary of the ovaloid is also the norm of the matrix.

This makes it, for example geometrically obvious why the 0 matrix has norm zero and why the identity has norm 1.

>>11901392
>Then there exists at least an element k in whatever space you are working with such that k≠k, or k−k≠0
I don't think that's right. It can still just so happen that k = k for all k, but it cannot be assumed up front. Of course, the intuitive (semantic) notion of equality is lost, but I'm trying to see how any mathematical proof would suffer under this syntactically. Unlike other axioms, you never hear of "logical inference by the reflexivity of the equality symbol". But I suppose all knowledge of lost if we cannot assume this: we may prove 1 + 1 = 2, but if 2 ≠ 2 then 1 + 1 ≠ 2, which means our proof is incomplete until we prove that 2 = 2, which we cannot do. I suppose that is the fundamental issue: not that it inhibits proofs halfway through, but that a proof is never complete. Correct me if I'm wrong about this.

>>11901537
ok now I'm a bit confused
the norm you're talking about is the operator one right? where
||A|| = max ||Av|| over all ||v|| = 1, where ||v|| is the euclidean norm for vectors

and that's different from the one where you vectorize the matrix and take the euclidean norm of that thing, right?

im not sure which one the asker was referring to

>>11901529
You have a function, say f. Similarly to how it depended on a single variable if the domain was [math]\mathbb{R}[/math], it can now depend on 2 variables, say x and y. At no point do you need to define a direct relation between x and y, and in fact when you start seeing partial derivatives you'll see that the other variables are usually treated as constants, because as far as x is concerned y is just another number there, they are not involved with one another (unless you define them to be that way).
You can define a basic operation like the sum using this. For example, [math]f(x,y) = x+y[/math]. This is just the usual sum, and as you may know picking an arbitrary summand doesn't lock your choice for the second summand, they are not dependent of one another.

What you defined before indeed just sounds like you are mixing it up with function composition. Also, now it seems like you are actually talking about vector-valued functions, where the multiple components don't come in the variables but in the images. If you had a vector valued function of one component, you could actually write it like [math]f(x) = (a(x),b(x),c(x))[/math], which I think is what you meant. In that case, there is only one variable and each component function is still independent of one another. The functions a,b,c here are the usual real valued functions you are probably used to, and they can be defined however you want. You can even mix both notions and create a vector valued multivariable function, and in that case each component of the image would be a multivariable function that is defined by (for example) two variables, and in fact that's how you will usually do stuff like parametrizing a surface in [math]\mathbb{R}^{3}[/math], for example.

>>11901275
I think you can classify the connected Riemannian one-dimensional manifolds based on their completeness and diameter, if that's what you're asking.
Complete and diameter R? Circle with circumference R/2.
Complete and infinite diameter? Real line.
Incomplete and with diameter R? (0, R)
Incomplete and with infinite diameter? [0, infty).

>>11901579
*(0, infty) on the last line.

>>11901555
>the operator
There isn't "the" operator norm. Every norm induces an operator norm by the definition you posted. The 2-norm of a matrix is the norm induced by the 2-norm.

>and that's different from the one where you vectorize the matrix and take the euclidean norm of that thing, right?
This is called the Frobenius Norm and is different to the 2-norm. It is also NOT induced by any norm on the vector space, that makes it geometric meaning harder to understand.

>im not sure which one the asker was referring to
Unless he uses very non-standard naming the 2-norm on matrices is the norm induced by the 2-norm on vectors.

>>11901602
ok thanks for clearing up the confusion, seems like ive been mixing up some terms myself

>Do math whatever
>Intense need to jerk off
Am I the only one with this problem?
https://youtu.be/aSn1g-6h1OQ

>>11901545
>It can still just so happen that k = k for all k
If that happens then you have a reflexive relation. The definition of reflexive relation is [math]\forall k \in S: k \mathcal{R} k[/math], and the logical negation of that is [math]\exists k \in S: \neg (k \mathcal{R} k)[/math]. If it is not reflexive then by definition such an element has to exist. It'd be like saying a set is not open but stating I still can't claim there's a point that's not in its interior, or saying a number is irrational but stating that I still can't claim that it can't be written as a fraction of integers. At that point you would be saying that we don't know whether it is reflexive or not, and then whatever happens in that set would be nothing but a guess.

The rest is correct, it's basically what I was trying to get at. Even if you were to "solve" an equation, you still can't make any conclusions because a number wouldn't necessarily be the same as the value it is equal to.

i know you gusy May not believe this but i havent slept in months. No micro-sleep,no naps,nothing.
How do i get myself examined by scientists or doctors?
I kinda want to find out how I can thrive,as I do,on no sleep.

in statistical physics if we have N identical and independant particles with each particle that could be in L+1 different states
where the state 0 = -A, with A>0 and all the other states being equal to 0
I can calculate the partition function being Z= L + exp(beta*A)
But the correction of the exercice says that is Z1 and Z = Z1^N
why is that?

>>11901622
But I am not replacing the axiom by its negation, I'm making no claim on the reflexive property of x whatsoever. But it brings us to the common conclusion that no proof would ever be complete. Thanks for the discussion.

>>11901646
If you ever have some y with x = y, then you can prove reflexivity of x from symmetry and transitivity
so the only way you could have a system without reflexivity but still have symmetry and transitivity
is by disallowing anything to equal x, including x so you would have the negation of reflexivity

>>11901664
>If you ever have some y with x = y, then you can prove reflexivity of x from symmetry and transitivity
How? Don't you need to know that y = y for that?

>>11901679
x = y implies y = x by symmetry
and then x = y , y = x implies x = x by transitivity

>>11901685
Of course, I realized it as soon as I hit post. Still, without knowing y = y this doesn't guarantee that x = x.

I'm not a physicist so please excuse me for this.
In the double slit experiment, when they use a sensor to detect if an electron goes through one slit, the resulted pattern will look like that of particles.
People say that the act of observation change the behavior of the electron. But can it be because there is no way for a sensor to detect an electron without affecting its behavior?
Why do people associate this experiment with the "tree was falling in the wood, since you hear no sound, was the tree falling or not?" thought experiment? They are fundamentally different right?
One is about the limitation of our observing device, the other is more of a philosophical question.

>>11901695
but i never used y = y in the proof

>>11901707
True, but you want this to hold for any y imaginable. But without reflexivity there may be y such that y ≠ y, in which case we obtain x = y ≠ y = x hence x ≠ x for any y that has x = y. It is like I said in my second post: reflexivity is never "used" in a proof; but it is necessary to ensure that the proof is complete.

>>11901717
No.

>>11901717
i can use my symmetry transitivity proof to show that y = y as well, the only thing you need to get reflexivity for something is symmetry, transitivity and some other element that equals it
if you have x = y and y =/= y then you just have a contradiction, since x = y implies y = y

>>11885791
In colonizing a habitable moon of a gas giant, would the gas giant's gravity be a considerable inconvenience in leaving/arriving at the moon?

>>11901728
>i can use my symmetry transitivity proof to show that y = y as well
You would need an element z such that y = z as well as z = z. If z is left unconstrained in its reflexive property (i.e. we don't know whether z = z or z ≠ z) then we don't know whether y = y either. And then for z you will need to do likewise. Reflexivity can only be proven through elements that are themselves reflexive.

>>11901775
no i dont need another element z, if i have x = y, then i have y = x by symmetry
so then i have y = x and x = y, so by transitivity i have y = y. If i commute the logical and then i get the proof for x = x.

I have [math]h : \mathbb{R} - {0, 2} \to \mathbb{R} : h(x) = \frac{(2x+1)^2}{x^2-2x}[/math]
and i'm being asked to find the preimage of 4 and 0 and define if there's any real number of the codomain that has no preimage.... What does this mean?

i already calculated the preimage of 4 and know it's [math]\frac{-1}{12}[/math] , i also calculated the preimage of 0 and it's [math]\frac{-1}{2}[/math] ... can 0 be the one with no preimage? because if i do [math]h(x) = 0[/math] then i end up knowing the values that make the denominator 0 in the function, which are [math]x = 0, x = 2[/math] and are excluded in the domain, is this right?

>>11901858
>What does this mean?
It means you have to check whether there's a value that the function doesn't touch.

>I also calculated the preimage of 0 and it's −12 ... can 0 be the one with no preimage
Nigga...

is it possible to see through people with radio wave ? like an MRI
>inb4 Xrays
something less dangeous

>>11885791
How do I prove that a sequence of functions does not converge uniformly?
I'm trying to prove that the sequence with nth term
[eqn]f_n(x) = \frac{1}{nx+1}[/eqn]
Doesn't converge uniformly on (0,1). I think I can do it with the supremum criterion (if fn converges uniformly then [math]M_n = Sup_{x \in (0,1)} (f_n(x) - f(x)) \rightarrow 0[/math] as [math]n \rightarrow \infty[/math])

>>11901893
oh fuck i expressed it bad, but you said that chack values where the function doesn't touch, so that has to be 1, right? because it's not defined in the domain

>>11901916
You absolutely should use the supremum criterion. Just check for different regions of the domain of the function where it converges uniformly.

>>11901934
Now it was me who worded it wrong. I meant to say, check which values aren't in the image of the function.

>>11901938
The problem I have using the supremum criterion is that I find everything that follows "weird" to say the least.

Clearly: [eqn]\frac{1}{nx+1} \xrightarrow{pointwise} 0[/eqn]

Thus:

[eqn]M_n = Sup_{n \in (0,1)} \Big| \frac{1}{nx + 1} - 0 \Big|[/eqn]

Now, wtf happens with that supremum? Can I formally state it simply doesn't exist, and thus the function can't converge uniformly?

How would I find a generalized function f such that 2*pi*t*f=dirac's delta? (being t the independent variable). I think I read the answer should be something like delta/2*pi*f + Co*delta with C0 a constant. that constant originating because of the simple zero in t=0. But I might be wrong. I'd appreciate any help

>>11901968
>doesn't exist
[math]0 \leq \frac{1}{nx+1} \leq 1[/math] tho.
In fact, that's always the supremum.

>>11902018
I meant delta/2*pi*t. Still, I'm not certain that's the correct answer.

>>11902018
>>11902026
What?
You want a distribution [math]f[/math] such that, for any test function [math]\phi[/math], [math]2 \pi t f ( \phi) = \phi(0)[/math]?

>>11902041
Yes

i dun git it

i dun git it 2/??

>>11902077
literally can't be more spelled out for you than this
matrix form of T (wrt standard basis) is given by its image on the standard basis, which are the y_i's
better yet, use linearity to decompose the vectors they give you

>>11902100
sooooo?

>>11902019
Dude, no, if x is near 0 the supremum grows without bound.

>>11902109
domain is (0,1), so it shouldn't blow up

>>11902055
Recall the commutation relation [math][ \frac{d}{dt}, t] = 1[/math], where the isolated [math]t[/math] is the multiplication by t operator.
Then, by setting [math]g = \frac{d}{dt} f[/math], [math]\phi (0) = \langle 2 \pi t \frac{d}{dt} g, \phi \rangle = \langle 2 \pi g, - \frac{d}{dt} t \phi \rangle = \langle 2 \pi g, - t \frac{d}{dt} \phi - \phi \rangle[/math].
So we set [math]g =- \frac{1}{2 \pi} \delta[/math] and then we get [math]\langle \delta t \frac{d}{dt} \phi + \phi \rangle = - 0 \phi ' (0) + \phi (0) = \phi (0)[/math], if I didn't fuck anything up.
>>11902109
[math]n \geq 0[/math], [math]x \geq 0[/math] , so [math]nx + 1 \geq 1[/math], isn't it? Numerator constant, denominator bounded below, fraction bounded above?

>>11902097
Plug and chug:
[math]\nabla f(\mathbf{x}_0) \cdot (\mathbf{x} - \mathbf{x}_0) = 0[/math]
where [math]\mathbf{x}_0[/math] is the given point

>>11885791
>>11885825
>>11890122
>>11893982
>>11896591
>>11899837
>>11901723
>>11902128
>>11902019
Please stop posting my waifu for others to see. Thank you.

>>11902136
ok, got the vector., what about the plane?

Is architecture a STEM field?

almost done for the day guys, sorry for the sophomoric questions

>>11902143
No way lmao. What's the point of even posting here if I can't post cute Remilias?

>>11902128
Shit yes. So the supremum is always 1, my fuck up.
I can argue that as n goes to infinity the supremum stays at one right?

>>11902128
Thank you (for the distribution question).

>>11902190
also, I've evaluated this for x=-3, y=-3, z=-2, and got -4.5, but it said it was incorrect.

>>11902171
you just take the point plus its linear approximations in each variable

>>11902219
isn't that what I did here?: >>11902190

I got that equation, then I subbed values in for x=-3, y=-3, z=-2, and arrived at -4.5, but it was wrong.

>>11902236
Replace [math]\frac{xy}{z}[/math] with -9/2

>>11902268
I tried '-4.5' as my answer but it failed

>>11902283
Evaluate the partials too.

>>11902294
I did, I set x=-3, y=-3, z=-2 for the entire equation. the partials just evaluate to 0 (-3 + 3), (-3 + 3), (-2 + 2), unless I'm doing something wrong there.

>>11902294
once I get it I should be able to solve the remainder of the problems for tonight, I'm getting all these linear approximiation questions wrong. thanks for helping

>>11902077

bumperino

>>11902268
>>11902294
>>11902297
>>11902327
got it, thx for halp

>>11902171
>>11902190
solved

>>11902097
bump

>>11902097
solved

>>11902077
someone please for the love of god help me with this one

I heard that multitasking is bad but Can listening to youtube videos while playing games damage my brain?

>>11900405
please respond

>>11902077
>>11902405
[eqn]T\left(\begin{bmatrix} a \\ b\end{bmatrix}\right) = a\cdot T\left(\begin{bmatrix} 1 \\ 0\end{bmatrix}\right)+ b\cdot T\left(\begin{bmatrix} 0 \\ 1\end{bmatrix}\right) [/eqn]

Is this true?
If [math]X[/math] and [math]Y[/math] are topological spaces, then [math]X \cong Y[/math] if and only if [math](X \times Z) \cong (Y \times Z)[/math] for all topological spaces [math]Z[/math].
Did a quick sketch of a proof that kinda convinced me it's true, but I'm not entirely sure.

>>11902626
ok,I've got the correct answer for that one, but I still don't know how to solve the first one. sorry..

>>11902626
nevermind about >>11902664, I've got them both now. Thanks!

>>11902653
Forward direction is automatic. For the reverse direction, let [math]Z[/math] be a one point set. Then [math]X\times Z\cong X[/math], and the result follows quickly.

>>11902671
Ok, my sketch was in the right direction. Thanks for confirming.

Does anyone know of some youtube channels like this one?
https://www.youtube.com/channel/UCEszlI8-W79IsU8LSAiRbDg/videos

>>11901794
You're not wrong. Using only these steps you can show that x = x without questioning whether y = y. Still, if y ≠ y, an additional transitive step will show the opposite, so x equals and does not equal x at the same time. Maybe this is a flaw in our definition; after all it stands to reason that if x equals y and y doesn't equal itself then x doesn't equal itself either. But really this shows once more how the axiom of reflexivity can be ignored in proofs yet needs to exist formally to avoid contradictions.

>>11902555
>>11902859

>>11901858
There is no x s.t. -5<h(x)<0
Solving for x gives you a quadratic where the discriminant is h^2+5h = (h+5/2)^2-25/4. This will be negative for -5<h<0, meaning that there's no real x satisfying the equation.

If you graph it, the discontinuities at x=0 and x=2 splitting the graph into 3 regions. For x<0, h(x)->4 as x->-∞, and it has a minimum at h(-1/2)=0, so h(x)>0 in this region. For x>2, h'(x)<0 (i.e. it's monotonic decreasing); again h(x)->4 as x->∞, so h(x)>4 in this region. For 0<x<2, it has a maximum at h(1/3)=-5, so h(x)<-5 in this region.

Thus the image is [0,∞]∪[-∞,-5]∪[4,∞] = [-∞,-5]∪[0,∞] = R-(-5,0).

>>11901518
thanks, got it fixed because you made me look at the architecture again and I've noticed that I fucked up the embedding layer

>>11900405
>>11902555
>>11902928

>>11902128
*[math]f = \frac{d]{dt} g[/math].
Well, anon probably noticed it.

>>11900405
>>11902555

Looking to to a text mining project with machine learning using recipes and ingredients as datasey, to determine what recipe best matches the input ingredients. Would this even count as machine learning if you consider the recipes as classes, ingredients as features and set of ingredients/input as a feature vector?

It seems overkill to me to use ml algorithms for such a trivial task but it still counts as ML, right?

Should I get a Macbook or a windows laptop for programming?