/sqt/: Stupid Questions Thread

I have a value of right ascension and declination and need to find "pixel size on the sky" in arcsec/pixel from these (Context is aperture photometry) but I can't find any information about how to do this. Is this just (RA/dec)/1 with both values in arcsec?

>>8409795
Is well do /SQT/ trheads, but not as often.

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>>8409795
I am dumb so I need help with this

Say I have an electric motor that can put out 1492 watts of power (about 2 hp). If I put it on a small bicycle, how can I use this info to determine force, acceleration, velocity, etc..? Say the bike with a person on it weighs 150lbs ( about 68kg of mass)

I know Power = Force x Velocity but then what?

I've tried picking an arbitrary velocity to find Force, but I am unsure what this result represents.

Say friction is negligible and velocity is at 9 m/s. So 1492 Watts = Force (N) * 9 m/s

which leads to Force = 165.7 Newtons.

Is it appropriate to move onto F=ma with this result? That would lead to acceleration = 2.44 m/s^2 but I am unsure of these calculations.

Thanks

What does the "a" represent in a Taylor series?
It's clearly important, but none of the material I've read mentions what it signifies.

>>8409795
it's quite simple, really. You take the number of elements in the bag which will be X+T factorial and divide that by the total number of elements in the sample which would be X+T! multiplied by S+X factorial.

>>8410693
if you mean the a where the taylor series is sum c_n (x-a)^n , it means the taylor series is 'centered' at the point a

https://en.wikipedia.org/wiki/Taylor_series#Definition

you can write down the taylor series for a function at any given point but the series can change based on the point (the coefficients c_n are derivatives evaluated at that point)

>>8410693
The Taylor series evaluates f(x=a)

>>8410420
Yes. Use P=Fv
Then use F=Ma

>>8410420
But take in mind that the acceleration you have obtained is only for a particular instant, as P provided is a constant, so F would vary, and thus a.

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>>8410713
>>8410717
Ah okay thank you anons

What is the IQ cutoff for brainlet? I say 140.
139 IQ is King of the Brainlets.

>>8410731
140 is the average IQ for Sudan, a country which can barely feed itself. Average for the United States, Australia, and China is around 161, 92, and 155 respectively. Brainlet would probably be around 150 and King of Brainlets would be 159.

>>8410738
>140 is the average IQ for Sudan, a country which can barely feed itself

That doesn't have anything to do with IQ, it has to do with shit tier environment, shit tier land, and shit tier culture. Smart people will do anything for basic resources and to protect their people too, including going to war.

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>>8410709
So a can be anything but I'll get the most accurate results if I make it close to the x value I'll use?

Also, how do I calculate the error?
All the stuff I find is incredibly unclear, I have no idea what value to use for M and c.

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>>8410738
That's wrong though.
Why don't brainlets just move to Africa and be relative geniuses?

>>8409795
It's been a while since I did this kind of shit but can't you just use the Bayes theorem?

P(A|B)=P(B|A)*P(A)/P(B) where A is the event "bag contains X white balls" and B is the event "got Y white balls from a sample of Z balls with replacement". I'm very rusty so what I'm about to write might be complete shit but I'll give it a shot, instinctively I'd say:

P(A) = 1/T
[math]P(B)=\frac{1}{T}\sum_{n=0}^{T}(n/T)^{Y}((1-n)/T)^{Z-Y}[/math]
P(B|A) = (X/T)^(Y)*(1-X/T)^(Z-Y)

>>8410744
>So a can be anything
you can pick any a but you're restricted by how many derivatives exist at that point

> I'll get the most accurate results if I make it close to the x value I'll use?
yes

>Also, how do I calculate the error?
>All the stuff I find is incredibly unclear, I have no idea what value to use for M and c.
it tells you what they are. the error is defined AT A POINT c (which you choose), and M is ANY upper bound for |f^(n+1)(x)|, the absolute value of n+1'th derivative of f in the interval between a and c.

>>8410758
I still don't understand what M is, that's just a more complicated version of the same explanation.

>>8410747
Forgot to conclude, in the end you'd have
[math]P(A|B)=\frac{(X/T)^{Y}(1-X/T)^{Z-Y})}{\sum_{n=0}^{T}(n/T)^{Y}((1-n)/T)^{Z-Y}}[/math]
If we have 3 balls, 5 samples of which 4 turn out white, and we're looking for the probability of 1 ball being white and two being black we get:
[math]P(A|B)=\frac{(1/3)^4*(2/3)}{(1/3)^4*(2/3)+(2/3)^4*(1/3)}[/math]

Which amounts to 0.11111, in other words there's a 89% chance that you're in the "2 white 1 black" configuration and 11% that you're in the "1 white, 2 black" configuration which seems about right

>>8410769
example:
if f(x) is x^4
f^(1)(x)=4x^3
f^(2)(x)=12x^2
f^(3)(x)=24x

and you pick a=1

then the taylor polynomial of order 2 at a is
f(1)(x-1)^0+[f^(1)(1)/1!](x-1)^1+[f^(2)(1)/2!](x-1)^2
=1+4(x-1)+6(x-1)^2

say we want a bound on the remainder at the point c=0, then since the third derivative of f satisfies |f^(3)(x)|=|24x| <= 24 in the interval [0,1] between a=1 and c=0, we can use M=24 (in fact any M>=24)

and so the 3rd remainder at the point c=0 is bounded by:
|R_n(c)| <= 24/(3!)|0-1|^3=4

and as a sanity check we can see that |R_n(c)|=|f(c)-p_3(c)|=|f(0)-p_3(0)|=|0-1|<4

>>8410776
>>8410747
Fuck, it's [math](1-n/T)^{Z-Y}[/math] not [math]((1-n)/T)^{Z-Y}[/math]

>>8410776
Last post, the formula
[math]P(A|B)=\frac{(X/T)^{Y}(1-X/T)^{Z-Y})}{\sum_{n=0}^{T}(n/T)^{Y}(1-n/T)^{Z-Y}}[/math]
is easy to understand: on top you have the odds of getting that sample (Y white out of Z picked) in the configuration where you have X white balls and T-X black balls, and at the bottom of the fraction you have the sum of the odds of getting that sample for all configurations.

>>8410779
woops
should say '2nd remainder'
|R_2(c)| <= 24/(3!)|0-1|^3=4

and

|R_2(c)|=|f(c)-p_2(c)|=|f(0)-p_2(0)|=|0-1|<4

>>8410779
Making it more complicated each time you try explain certainly won't help!

>>8410794
i dont know what else to say, its literally any upper bound for the function on an interval

do you understand what it means for a function to be bounded?

>>8410796
Nope, never seen it used before.

>>8410798
you've probably got some things you should review before trying to learn taylor's theorem then

https://en.wikipedia.org/wiki/Bounded_function

its just a number that tells you how big or small the function can be

can you figure out a bound
f(x) =x
in the interval [0,1]?

this just means any number such that |f(x)|<M whenever x is in [0,1]

>>8410802
>things I should reiview before trying to learn Taylor's theorem
This is how my university teaches.

So for f(x) = x^2/3 and n = 4, M = the fifth differentiation of f(x) where x = 9 if a is 8 and c is 9?
The fifth differentiation of f(x) is positive, btw.
Actually, it'd probably be x = 8...

And c would be 9 if I was calculating the error for x = 9?

>>8410746
DAS RACIST

EE or CS, wich is the smarter pick and why?
No
>W/E you like the most

>>8410813
>So for f(x) = x^2/3 and n = 4, M = the fifth differentiation of f(x) where x = 9 if a is 8 and c is 9?
no, M is any real number which is larger than the absolute value of the fifth derivative in the interval [8,9]

i cant tell if you meant x^(2/3) or (1/3)*x^2

if its the second one the fifth derivative is 0, and so |f^(5)(x)|=|0| so you can take any M >= 0

if its the first one then
f(x)=x^(2/3)
f^(1)(x)=(2/3)x^(-1/3)
f^(2)(x)=(-2/9)x^(-4/3)
f^(3)(x)=(8/27)x^(-7/3)
f^(4)(x)=(-56/81)x^(-10/3)
f^(5)(x)=(560/243)x^(-13/3)

when x increases, this function f^(5)(x) decreases, and so an upper bound for |f^(5)(x)| on the interval [8,9] is |f^(5)(8)|=|(560/243)8^(-13/3)|, and so you can take that number as your M value

>And c would be 9 if I was calculating the error for x = 9?
yes

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>>8410829
this is a pic of the fifth derivative on [8,9], and you can see the biggest value it can be is at x=8

>>8410829
Ah, managed to calculate it.
4.6883*10^-6 seems like surprisingly high accuracy, but I guess people do often confuse the Taylor Series for functions that equal functions only on an interval!

What is a Boltzmann Brain?
I have no idea what is or what it does.

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>>8411178
I'm trying to help a friend out with math but we can't figure it out. Any help, he says he have to use Excel

>>8409795
> How do you approach this type of probability problem?
It was answered at the end of the last thread (which has hit the bump limit but hasn't gone off the end yet):
>>8410323

> That's a different (and harder) problem. Also, you need to know the probability of picking a white ball when filling the bag.

> Assuming that black and white balls are equally likely when filling the bag, then:

> Let p[i] = (i/10)^2 * (1-i/10)^4 * C(6,2)/(2^6) * C(10,i)

> The probability of there being 5 white balls in the bag when you get 2 white balls out of 6 is
p[5]/sum[i=0:10](p[i]) ~= 0.278

> It's feasible to check this empirically by enumerating all (2^10)*(10^6) possible cases.

>>8411178
>>8411186
What do you mean you can't figure it out? All you have to do is add up all the monthly expenses and deduct the result from his income. The only part that's above addition level is calculating the monthly payments on car and federal loan but you don't even have to do that yourself

[math]\frac{2^x+4^x}{2^{-x}+4^{-x}}[/math]
Please help, i'm new to this. Result is [math]8^x[/math].

>>8411628
Do you know factoring?

>>8411632
Nvm I'm retarded and read it as x^2 and x^4

>>8411632
yes but i always get stuck in an infinite loop of factoring and re-factoring

>>8411628
Start with this
[math]4^x=(2^2)^x=(2^x)^2[/math]
[math]2^x+4^x=2^x+(2^x)^2=2^x(1+2^x)[/math]

>>8411628
I won't spoonfeed too much you but you'll have to use >>8411639 and [math]1=2^x2^{-x}[/math]

>>8411628
I done it woo!! that was hard

>>8411664
Good for you, i'm still doing it

>>8411666
I could post the answer?

>>8411667
If you want. I will look at it later

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>>8411671

>>8411674
>people who post disoriented photos
literally worse than hitler

>>8411674
cute smiley faces bro but this gave me neck cancer

>>8411675
>>8411676
posted it from my phone so i couldn't spin it around
>try saving then rotating plebs

>>8411674
>>8411678
Ooooh m8 i will never furiously try to get rid of fractions again. Got it as well, thanks

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let C,D be two matrices with integer entries satisfying (C^T)D=(D^T)c (T meaning transpose)

why must we have det(iC+D) non-zero?

Can someone explain to me what a bilinear form being non-degenerate means on a infinite dimensional vector space?

Wikipedia puts it as the map
>v ↦ (x ↦ f(x, v))
is an isomorphism

But I am not familiar with this notation.

Where on another article they put is as:
>B(v, w) = A(v)(w).
>This form will be nondegenerate if and only if A is an isomorphism
But what is A(v)(w)

Given: a, b reals; |a| < |b| ; a < x =< b^2

How demonstrate than 0 =< x^2 =< b^2 ?

An answer of a precedent thread: "Minus all by a, so you have 0 < x-a =< b-a , square this, then apply that square will always be non zero so the ineuqality holds.", in follow this i have 0 < x^2 - 2ax + a^2 =< b^2 - 2ab + a^2 and what ? How i land to 0 =< x^2 =< b^2 ?

It's for an exercice with this numbers -1 < x =< 3 and i must find what is for x^2.

>>8409795
Please help me understand this:
Suppose I have a ring like [math]\mathbb{C}[x][\sqrt{x(x-1)(x-2)}]=\frac{\mathbb{C}[x,y]}{\left<x(x-1)(x-2)-y^2\right>}[/math]
How do I prove it is integrally closed domain?

I'm also not sure if it's a GCD domain?

>>8409795
That's just depressing

>>8411899
>[math]f(x,y)=0[/math] for all [math]y \in V[/math] implies that [math]x = 0[/math].

Me and two friends played black jack and all of us ended up with a score of 20 after all of us has asked for a third card. What is the probability of that happening?

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what is the best way to run? And why is it this one? Your hand will propel the air downward, providing lift hence reducing the friction.

You also don't waste as much energy to moving your hand back and forth while maintaining this aerodynamically superior stance.

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>>8411953
100%, obviously.

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Calc 3

When splitting up area D into two type II regions, one of the splits becomes negative.

I thought with integrals the end result is always positive? Since it represents area?

How is the final answer for volume negative as well?

>>8412035
Correction, they are two separate volumes, not areas. My bad.

Still, how is the final answer negative at all for volumes?

>>8412042
I guess negatives and positives don't matter with double integrals

>>8412063
I remember now
You need to take absolute value for actual area.

>>8412035
> I thought with integrals the end result is always positive? Since it represents area?

For an area integral, the value is guaranteed to be positive if the expression being integrated is always positive within the area. That's true for #55 but not for #56.

In #56, the region where y is negative is larger than the area where it's positive. Not only that, but the region where y is positive has proportionally more small values of y (the width of the region increases as y->0).

So intuitively, I'd expect the answer to #56 to be negative.

>>8412035
Your integration limits are wrong (part 3).
The integral can have a negative value, since you are not calculating solely the area [math]\int_a^b dA[/math], but you are calculating [math]\int_a^b ydA[/math], which can have a negative value if the function is only defined on the y<0 region, for example.

>>8409795
I've a question I need answering which I believe anyone who isn't innumerate as I am should be able to answer, but I am a poorly educated fellow.
I believe it may be to do with plotting curves and shit. I'm sure it's simple if only I knew how.
I have a 4000 pixel wide rectangle I wish to divide into 11 sections. I want the first section on the far left to be 664 pixels wide, and the last section on the far right to be 272 pixels wide, and the remaining nine sections to get gradually smaller in equal increments so that the second section is as much shorter than the first as the third is than the second, and so on until the last (11th) section is as much shorter as the preceding section as all the others are as their preceding section.

>>8411910
That is only true for finite dimensional spaces, which is why I specified that I am looking for the definition for infinite dimensional spaces.

Plus, they specify that it has to be an isomorphism to subset of V*.

So I am confused as fuck as to what function is supposed to be isomorphic to a subset of V*.
I've tried looking into various books, but the restrict themselves to the finite dimensional case.

Here's the articles that I mentioned:
https://en.wikipedia.org/wiki/Degenerate_bilinear_form
https://en.wikipedia.org/wiki/Bilinear_form
https://en.wikipedia.org/wiki/Dual_space

These all describe it into a form or another.

>>8412111
> the remaining nine sections to get gradually smaller in equal increments so that the second section is as much shorter than the first as the third is than the second
By "as much shorter", do you mean a constant difference or a constant ratio?

For a constant difference, you have an arithmetic sequence: a,a+d,a+2d,a+3d,...

For a constant ratio, you have a geometric sequence: a,a*r,a*r^2,a*r^3,...

Each of these has a closed-form expression for the sum of a given number of terms. So knowing the first term and the sum of 11 terms, you can solve for a and d or a and r.

TBC

>>8412181
a constant difference, so that if the second section is ten pixels longer than the first, the third should be ten pixels longer than the second.

Another way of describing it, although I apologise for not writing it correctly is -

if 0 is 0, 1 is 272, 11 is 3336 and 12 is 4000, what are 2,3,4,5,6,7,8,9,and 10?

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I have a stupid question about Calculus III/Vector Calculus! Generally, I have to understand the concept to practice and engage it. However, my professor is really shit at teaching, and he is more fond to write down formulae, and immediately goes over textbook problems rather than explain what the formula(e) mean(s). Pic related. I didn't do TOO good on 3D space and vector exam (80% or something). I mostly just went over practice problems and did them until I got a fair understanding of what's being asked.

My question relates to self studying in a progressive way. I'm reading through Advance Calculus Demystified, and it aids me more than my current textbook. What can also help me self study to understand ideas in a conceptual level that isn't fully formulae? What can help me "be" smarter in understanding regurgitated formulae? Sorry for the long tl;dr.

And a bonus question! Could someone explain vectors in 2d and/or 3d space? As stated before, my professors talked about vectors without actually talking about what it is. I understand it's a form of direction that starts in origin, but I don't understand beyond that. It also perplexes me that parallelograms can be conveyed using vector coordinates. SORRY FOR THE HUGE TL;DR AGAIN

>>8412181
that's a great help, thank you

>>8412181
For an arithmetic sequence, the sum to N terms is
S[n] = n*(x[1]+x[n])/2
where x[1]=a and x[n]=a+(n-1)*d

E.g. if x[1]=664 and x[11]=272, then S[11]=11*(664+272)/2=5148. Which isn't equal to 4000. So you'll have to give up on one of the constraints.

Omitting the last one and using x[1]=664 and S[11]=4000 gives 4000=11*(664+x[11])/2 => 664+x[n]=8000/11=727.27... => x[11]=727.27...-664=63.27...
=> d=-60.07272...

For a geometric series, the sum to N terms is
S[n]=a*(1-r^n)/(1-r)
x[1]=a, x[n]=a*r^(n-1)

If you put a=x[1]=664 and S[11]=4000, then
4000=664*(1-r^11)/(1-r)
=> (1-r^11)/(1-r)=4000/664
=> r=~0.86977
=> x[11]=~164.5

>>8412197
If the first is 272 and the sum is 4000, then then increment is 18.32727..., meaning that the last is 455.2727...
The complete list of widths is
272
290.32727
308.65454
326.98181
345.30909
363.63636
381.96363
400.29090
418.61818
436.94545
455.27272
Accumulating gives:
0
272
562.32727
870.98181
1197.96363
1543.27272
1906.90909
2288.87272
2689.16363
3107.78181
3544.72727
4000.0

>>8412075
>>8412079
Thank you. Integrals were explained to me as areas and volumes. I only realize now that integrals are more than that

>>8412252
You've helped me no end. It is visually very simple. Mathematically, I had no idea. Thank you very very much.

>>8412156
Ah, my bad.
>v ↦ (x ↦ f(x, v))
Means the map
[math]V \to V^*[/math]
defined as
[math]v\mapsto f(. ,v)[/math]
should be a literal isomorphism between [math]V[/math] and [math]V^{*}[/math] as vector spaces (yes, which is not guaranteed by injectivity and [math]\dim V = \dim V^*[/math] alone).

>>8411905
Halp, where to look?

>>8412323
elliptic curves are irreducible so the ideal they generate are prime so the quotient is an integral domain

>>8412301
> Integrals were explained to me as areas and volumes. I only realize now that integrals are more than that
Well, the main point here is that areas and volumes can be negative.

E.g. if area is base times height, base is always positive, and height can be either positive or negative, then the area can be positive or negative.

Often we're only interested in the absolute value of an area or volume, ignoring its sign. But when it comes to integration, sign matters.

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Why do they draw a line there? They just said x and y are vectors in n-dimensions. Doesn't their drawing imply 2-dimensional vector? It really messes up with me cause then when someone talks about a line segment between 2 vectors that image pops in my mind but then I'm like "um, where's [math]x_5[/math] on my image?" To my understanding there's no way to visualize this when it goes over 3 dimensional vectors, and this just confuses me

Do I misunderstand this, am I autistic or what?

I wrote a small program and published it under the GPLv3. I am now writing a manual in LaTeX mainly because I want to also turn it in for a university assignment (just the manual, not the program). Would I need to choose a license for that at all, and if so, which should I choose? I don't know anything about documentation licenses and was wondering what my options are.
I'm not yet sure if I want other people do be able to change the documentation without telling me what they're going to change.

>>8412354
x and y are vectors which can be interpreted as points in n-space

the line drawn is the line consisting of all points in n-space between x and y

>>8412359
But that space where is 2D space

>>8412362
>But that space where is 2D space
english please

>>8412362
s/where/there

>>8412364
I meant "there" instead of "where"

>>8412369
yes a line is 2d space, that's what's drawn

what are you confused by?

do you understand what a subspace is?

this is like a subspace except its an affine space because it doesnt have to contain 0

>>8412371
1d space*

>>8412371
>what are you confused by?
How did they draw [math] x \in \mathbb{R}^n[/math] in a 2D space

>do you understand what a subspace is?
Not really

>>8412322
Thanks. That's exactly what I wanted to know.

>should be a literal isomorphism between [math]V[/math] and [math]V^*[/math]
That makes sense, but the 3rd article is confusing me here.
While on both the first and second article they only mention it should be an isomorphism, the 3rd article mentions this:

https://en.wikipedia.org/wiki/Dual_space#Bilinear_products_and_dual_space
>If the bilinear form is nondegenerate, then this is an isomorphism onto a subspace of V∗. If V is finite-dimensional, then this is an isomorphism onto all of V∗

Are they talking about the bilinear form here still or is the [math]\Phi[/math] they define here something else?

>>8412375
why do you keep bringing up 2d space? a line is one dimensional

>>8412384
Cause the points have 2 coordinates, and so does every point on the line.

>>8412386
no, the points have n coordinates because theyre from R^n...

the line is one dimensional because every point on the line can be specified by some number t in [0,1]

>>8412389
>no, the points have n coordinates because theyre from R^n...
But the paper is 2D and I can give exact coordinates of those drawn points using 2 numbers. How do they have n coordinates?

>>8412395
> I can give exact coordinates of those drawn points using 2 numbers
then you'd be talking about a plane in R^n where every point has n coordinates but can be specified by two numbers since the plane is two dimensional

>How do they have n coordinates?
because x and y were chosen from the vector space R^n

>>8412405
>then you'd be talking about a plane in R^n where every point has n coordinates but can be specified by two numbers since the plane is two dimensional
Are you saying n = 2? I have no idea what you're saying otherwise.

>>8412407
no, it's for any n

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Is a black hole a disc, a sphere or a point?

inb4 yes

>>8412411
Is this related to subspaces? Cause I don't really understand the concept. Why can you represent vectors in n > 2 in 2 dimensions?

>>8412412
All those idiots who sacrifice UX for their retarded password constraints should fuck off the internet desu

>implying I even give a shit if someone finds the password to this service I'm going to use only once

>>8412413
they're not representing n dimensional space, they're representing the one dimensional space between the two points in R^n

>>8412418
Ok, I think I got you know: The points are N-dimensional, the line is 1 dimensional, and the plane they're represented on is 2 dimensional

>>8412422
yes

>>8412423
10x bro

>>8412383
I've always thought that [math]\dim V = \dim V^*[/math], but wow, they say:
>Thus if the basis is infinite, then the algebraic dual space [b]is always of larger dimension (as a cardinal number) than the original vector space.[/b]
Which means it can never be an isomorphism. Interesting. So it seems that definition is actually the same >>8411910 except you can't reformulate it in terms of some isomorphism between [math]V[/math] and [math]V^*[/math].

https://en.wikipedia.org/wiki/Dual_space#Infinite-dimensional_case
Pretty interesting, thanks for your question, anon

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>>8412428
>he didnt know the dual of an infinite space is bigger than the original space
pls pick up a linear algebra book

>>8412434
>pls pick up a linear algebra book
Not him, but what's *the* linear algebra book (like Jaynes is for probability, Chong for optimization, Bishop for machine learning, etc.)

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>>8412457
hoffman kunze gets recommended a lot

i think it's unlikely something you need to know isn't in there if you're an undergrad

>>8412465
>tfw doing my master's but i still read undergrad books
thanks computer science BEng

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>>8412468
engineering isn't math so i don't know why you'd expect to be reading grad-level books

especially when in my experience engineers try to learn as little math as possible

>>8412354
> Why do they draw a line there?
Because the set of points z defined by z-y=a(x-y) forms a line.

> They just said x and y are vectors in n-dimensions. Doesn't their drawing imply 2-dimensional vector?
No. It implies that they're drawing on a 2-dimensional sheet of paper. They're not stating that n=2, in the same way that the positions they chose for x, y and z in the diagram isn't a statement that those points are at those specific positions. It's just an illustration.

> To my understanding there's no way to visualize this when it goes over 3 dimensional vectors, and this just confuses me
It's hard enough to visualise when it goes over 2 dimensions.

In cases where the number of dimensions doesn't really affect anything, it's simple enough to give a 2-dimensional example (or a 2-dimensional representation of a 3-dimensional example if necessary). When you're dealing with 4 or more dimensions, you just have to get used to not being able to visualise things.

>>8412428
>So it seems that definition is actually the same >>8411910# except you can't reformulate it in terms of some isomorphism between [math]V[/math] and [math]V^[/math].
That doesn't seem to be the case, on the first link:

https://en.wikipedia.org/wiki/Degenerate_bilinear_form#Infinite_dimensions
They mention a case of an injective, but not surjective form on a close interval, but with a function that satisfies the property that
B(f,g) = 0 for all g in V implies f = 0

The same article at the beginning defines it in terms of an isomorphism first and then say it is equivalent to saying
B(f,g) = 0 for all g in V implies f = 0 for finite dimensional spaces, so I assume the first definition (in terms of isomorphism) is the one that holds for infinite dimensional vector spaces.

If that is the case, maybe that is why they mention that is has to be subspace of V*?

What are the most mathematical definitions of convex set and convex function?

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>>8412482
>most mathematical

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>>8412478
>>8412418
But how do they draw this kind of sets? Where do they get this shape from? like if you have

u = [1,65,43,-21,53]
v = [-21,2,0,0,3,55]
and then a bunch of other points in this set

How do you draw a shape out of this? To my understanding, you put u and v wherever you want when you illustrate it, but then how do you get this shape?

>>8412500
what shape are you talking about? you seem very confused about what you're trying to accomplish

>>8412507
The shape in the picture I attached. When they try to show convexity they draw this kind of thing and say it's not convex because the line goes outside of the shape. How do you come up with this kind of shape for a set? Is it purely illustrative and there are no ways to get this from a given set?

>>8412512
>How do you come up with this kind of shape for a set? Is it purely illustrative and there are no ways to get this from a given set?
the shape is just some set not containing the line segment, if you wanted to you could list every single point in that set

>>8412521
>if you wanted to you could list every single point in that set
How?
How do you decide where to put an N-dimensional point on a 2D plane? How do you decide how close the points should be in 2D according to their N-D values? It just makes me think of dimensionality reduction like isomap or t-SNE or PCA but I know this is not the right framework to think in

>>8412526
>How do you decide where to put an N-dimensional point on a 2D plane?
the shape is just a subset of a plane, parametrize the points of the plane by two coordinates and then place them where they belong relative to two axes

>>8412529
Do you mind giving me an example? How would you place [math]x= [1,-5,3,10][/math] and [math]y= [-10,-3,0,2][/math] on a 2D plane/shape?

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>>8412534

>>8412535
So you literally just place them randomly independent of their actual values?

>>8412536
you can put them anywhere you want, but if you want to include more points they should be placed relative to x and y in a reasonable way

it sounds like you're trying to do something specific though and it makes it difficult to explain, either that or you just don't understand what an illustration is

>>8412542
But what's a "reasonable" way to place 3 points?

>>8412546
if x, y and the third point are collinear then you should probably draw all 3 on a line

if not you can draw it anywhere

>>8412548
Ok I see what you mean, thanks again anon

>>8412482
A set X is convex iff it's closed under the operation [math](a_i) \mapsto \sum t_i a_i[/math] where [math]t_i \ge 0, \sum t_i = 1[/math]. (You may see this in the two-variable version, which is equivalent but not quite as nice.)

A function f is convex iff [math]f \left(\sum t_i a_i \right) \le \sum t_i f\left(a_i \right)[/math].

>>8412480
For infinite-dimensional cases there just cannot be an isomorphism between [math]V[/math] and [math]V^*[/math], only an isomorphism onto (onto its image) which is the same as
>B(f,g) = 0 for all g in V implies f = 0

>>8412553
Oh, okay. Thanks.

>>8412336
But [math]y^2-x^2(x-1)[/math] generates a prime ideal too?
And [math]\frac {\mathbb{C}[x,y]}{x^2(x-1)-y^2}[/math] isn't integrally closed since [math](\frac y x)^2-x+1=0[/math]

Maybe you thought I was asking about an integral domain but was asking about integrally closed, https://en.wikipedia.org/wiki/Integrally_closed_domain

>>8412575
my bad, in that case since an elliptic curve E is nonsingular the local ring at any point is integrally closed, and so quotient C[x,y]/E is integrally closed

>tfw i'll never be able to use that black rectangle at the end of a proof in an academic paper because I can't prove shit with my maths

So I'm learning basic trig to re-affirm what I learned in high school. However, the textbook shows values such as:

cosine 60° 43'

It states that apparently the second value is 43/60, but it doesn't really explain what the value represents or where it's gathered from.

Can anyone give a brief explanation? Or at the very least, can someone tell me the name of the second value, so I can find out on my own?

>>8412706
60' = 1°

It's called a "minute"

>>8412706
Yes, second value is 43/60, it's in arcminutes
https://en.wikipedia.org/wiki/Minute_and_second_of_arc

>>8412725
>>8412729
Makes much more sense now, thanks anons.

>>8412594
Thank you

>>8409795
I'm twenty-three, I've been math illiterate almost all of my life and have taken a liking to getting the solution to algebra problems on KhanAcademy.

I want to go on and be able to understand stochastic calculus. Do I have a chance, or is it too late for me? I think math has been my calling, but I've failed to realize it because everyone told me that they weren't math people, so I thought I was the same way.

>>8412961
>23
>is it too late for me
Of course not, it's not athletics. You have, likely, >50 years to live with a functioning brain. Even if you have lower than average ability and even if it takes you 10 years to study whatever - you still will have over 40 years to use the acquired knowledge.

I have a digital scale with a div of .002 lbs. it can count by weight. I can place 10, 20, or 50 bolts on the scale and tell it how many there are. The scale will then count bolts as I add them. What's strange is that when I gave the scale the weight of 10 bolts it told me I had 100 total when I gave the scale the weight of 20 it told me I had 95 and when I gave it the weight of 50 it said 89. The bolts are more weighty than the div. I don't know the precision of the bolts but they should weigh about 0.02 lbs. how many bolts and why does my scale not have a div of 1 gram?

>>8412993
Your scale probabaly has a minimum capacity. If you're counting by weight your sample should be at least this value.

What is the constructivist alternative for the mean and intermidate value theorems?

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can somebody explain what he means by [math] n_1 \cdot a_2 [/math]?

does he just mean [math] (a_2)^{n_1} [/math]?

i think i'm good with algebra but this is just unusually hard to follow please help

how do i prove if Q= 0 then pVgamma =const

>>8413147
M is a monoid so it has some operation which is being denoted by +

then n1 * a2 = a2 + a2 + a2 + ... + a2 where there's n1 a2's in the 'sum'

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Is this car hatch a slider crank mechanism and is my kinematic diagram correct?

I have -1 < x =< 3 and i must find interval for x^2, i know it's 0 =< x^2 < 9 but how demonstrate it ?

>>8413449
x^2>=0 since x^2 is always non-negative

x^2<9 since x<3

>>8413456
x^2<= 9 since |x|<= 3

Im studying to be a doctor but I find the content ridiculously easy. I enjoyed chemistry and physics because you actually had to think a bit. Why is med students regarded as being brainiacs when its probably one of the easiest sciences?

>>8413475
>Why is med students regarded as being brainiacs when its probably one of the easiest sciences?
because med students have unreasonably large egos

>>8413475

Because money.

>>8413475
And i don't think there is an easiest science.

>>8413475
First year of an undergraduate program?

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The job was to calculate inverse bilateral transformation.
Can someone help me, why:
Z1 considered, when it was stated Z<|2|

>>8413488
Z>|2| sorry, wasnt it supposed to wait till for:
n<0 then it flips the convergence, and the poles you need to finds are the ones outside the convergence range

>>8413475
Arriving to a correct diagnosis based on clinical history, lab tests, and imaging tests is not easy at all. It requires years of experience with real patients to grasp the fundamentals of medical practice.
You haven't even begun, so don't get ahead of yourself.

>>8413504
>t. m3

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Is pseudosphere always finite or does its thinner part go on forever in general case? If it doesn't, does it always end with a hole (picrelated) or its walls can link up and form a pike?

Sorry, I am not a math person nor I am familiar with English math terms.

>>8413593
Got it. https://www.youtube.com/watch?v=AG6kN3w48jI Sorry for a really stupid question.

>>8413408
Please help

Physics major looking to go to applied math grad school. How difficult is the switch? How difficult would it be to pass the prelims without some of the more abstract courses

I've taken Calc1-3, ODE, PDEs, Complex analysis, Numerical analysis, and a graduate Fourier analysis course.

I'm looking at computational fluids, electromagnetics, and imaging.

>>8413862
you wont make it brainlet

>>8413862
You might make it

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>>8413971
>le won't make it meme

guess what? i WILL make it, you fucking neuronlet.

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>>8413979
stick to your free body diagrams you pathetic wavelet

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>>8413985
i bet you struggle using chain rule you disgusting amplitudelet.

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REAL QUICK Q

>About to diy a lightbox, which would sit a couple feet away from my face
Is lux higher as you get closer to a lightsource? I always see it talked about in terms of room size but if it's right on my damn face would I not be taking in a shitton regardless of my room?

>>8413971
>>8413985
>>8413993
>Asking for advice on 4chan
> ever

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>>8414046
get a load of this axonlet.

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>>8414046

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I'll step onto my scale and it tells me that weigh 150 pounds.

When I'm carrying my cat in my arms and I step onto the scale again, the scale now says I weigh 158 pounds. By this reasoning, any weight that I'm carrying weighs me down, but to what extent?

Let's pretend I had the most sophisticated weight scale in the entire world. I walk onto the scale naked and it reads something like, say, 150.32381828328 pounds exactly. Now, again while completely naked, were to carry a small coin in my hand (virtually weightless), would that value on the sophisticated scale change?

I would imagine that the very small coin would make me weigh a tiny fraction of a unit of weight heavier, but I'm unsure. I also believe that it could be possible that there is a point where a weight could be so insignificant that it would not change my weight because my arms are bearing the weight and it isn't affecting my body the way I'm using my whole arms and shoulder muscles to support my cat.

This has been bugging me, could somebody chime in on this?

>>8414126

Behold the stupidest question.

The answer is yes.

>>8413408
>>8413847
Please respond

>>8414126
> I also believe that it could be possible that there is a point where a weight could be so insignificant that it would not change my weight
Wrong. There would be a point beyond which the scale can't measure the difference, but that's not the same thing.

I apologize for being a brainlet, but why do I feel pressure between me and earth?
When two objects in space move by inertia and then collide they don't exert pressure on each other for forever, they just hit and then they're fine on their new inertial routes.

Then what's up with me and earth? Why can't we stop colliding? Is it what slightly changed geodesics make us do, right?

>>8414131
>>8414166
thanks for clarifying this for me. it really has been bugging me

>>8414170
I'm not sure I understand your question.
>When two objects in space move by inertia and then collide they don't exert pressure on each other for forever, they just hit and then they're fine on their new inertial routes.
When two objects in space collide, if the gravity between them is enough they stick to each other. In that case they would continue exerting pressure on each other forever. Basically you and the earth are an inelastic collision, so kinetic energy is not conserved.

How do you sample from a probability distribution? I see this shit with MCMC sampling but I don't understand. Can't you just generate a random number and put it in the probability function (if you know it)?

>>8414284
Probability distributions use a priori reasoning to probability and you get the expected results from there. Sampling is for statistical a posteriori modeling.

>>8414292
What?

>>8414294
You do a probability distribution when you already have the probability (or at least a good hypotesis of it) of the events in your sample space. Then you analyze its properties such as mean, variance, entropy etc. Sampling is used to get the probability distribution.

>>8414299
>>8414294
Wait, forget it I´m dumb

>>8414299
Oh. Really? So you only do sampling when you want to find the parameters of a distribution and you have access to a generator?

>>8414300
I'm confused

>>8414302
https://en.wikipedia.org/wiki/Pseudorandom_number_generator
Nothing I missunderstood you,

>>8413130
http://www.ams.org/journals/bull/0000-000-00/S0273-0979-2016-01556-4/S0273-0979-2016-01556-4.pdf

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Where is Wally?
...scientifically speaking

so [math]f(x) = x^2[/math] and [math]f'(x) = 2x[/math], yeah?

and [eqn]
f(1) = 1 \\
f(2) = 4 \\
f(3) = 9 \\
[/eqn]

and [eqn]
f'(1) = 1
f'(2) = 4
f'(3) = 6
[/eqn]

So the derivative should tell me the rate of change no? What does that mean? Cause if I go from f(1) to f(2), it seems like the result goes up from 1 to 4. What derivative can tell me that? I could say that look f'(2) is 4 so it means from f(1) to f(2) the result will go 4 times higher, but then that doesn't work further.

Reposting from /g/ /sqt/ after they mentioned you guys might know better:

Can someone help me with this question on my discrete math final? Been stumped for a while now and running out of time. This is a big part of my grade so any hint would be great.

Given an irrational number n, can it be assumed that irrational numbers x and y exist such that x * y = n? Construct a proof to support your answer.

>>8414320
We are dealining infinitesimals here, not unities. Derivative tells you a graph's tangent's slope.

What does variational mean in probability talk?

>>8414363
Yes. Assume a is a nonzero rational number, an * (1/a)n = n, product of a nonzero rational number and an irrational number will always be irrational. (Google that one if you feel the need to prove it as well.)

>>8414363
Lolz

>>8414378
So does f'(x) tell me that f(x) will change by f'(x) for very small changes?

so say I'm at f(2), will f(2.000000000001) change by roughly 2 * 2.000000000001 if f(x) = x^2 ?

What's a convex conjugate in simple terms?

>>8414284
Do you mean: how do you generate random numbers which have a specific distribution?

One generic approach is to generate uniform random numbers then apply the inverse of the cumulative distribution function.

But that only works if you can derive the cumulative distribution function and find its inverse.

If you can derive the function, then you can effectively invert it by using e.g. bisection to find values which map to the desired value.

>>8414387
Yes that's a good way to think about it. A better way to think about it is f'(x)=f(x)/x because slope equals rise over run. So it's more like f'(x) is the slope of the line tangent to the curve at x, or it's "instantaneous" slope. A way I like too look at it is dy=(dy/dx)dx or "a very small change in y (dy) is equal to the slope (dy/dx) times a very small change in x (dx)"

>>8414387
> So does f'(x) tell me that f(x) will change by f'(x) for very small changes?
f(x+δx) ~= f(x)+δx*f'(x)
if δx is small.
This follows from the definition of the derivative:
f'(x) = lim[δx->0] (f(x+δx)-f(x))/δx
=> f'(x) ~= (f(x+δx)-f(x))/δx (for small δx)
=> δx*f'(x) ~= f(x+δx)-f(x)
=> f(x+δx) ~= f(x)+δx*f'(x)

> so say I'm at f(2), will f(2.000000000001) change by roughly 2 * 2.000000000001 if f(x) = x^2 ?
It will change by roughly 2 * 0.000000000001 (i.e. the derivative multiplied by the change in x).

>>8414410
>It will change by roughly 2 * 0.000000000001 (i.e. the derivative multiplied by the change in x).
But the derivative is 2x not 2, no?

What happens if u have x/|x|?
For example, in the integral sin^2(x)cosx / (sqrt(cos^2(x))
Do i just cancel the cosines out or is there some special trick to deal with the potential negative 1?

I am re-reading my master thesis, I have to discuss it the 19th.
I saw that I made a mistake in the order of the references. I also saw I made a dumb mistake when introducing nmr, basically I said that COSY is used only for atoms that are linked by 1 or 2 bonds, and few lines after this I say that a COSY gives you information on the Hydrogen bonded to the N of a protein coupled with the C-alpha Hydrogen, and they are separated by 3 bonds (H-N-C-H). I will discuss my thesis with people who work exclusively on NMR.

How fucked am I? it's a minor mistake, but it shows I didn't care to actually understand what I was writing.

>>8414431
> But the derivative is 2x not 2, no?
Right, my bad.

If x is 2+ε, x^2 will be roughly 4+4*ε, x^3 will be roughly 8+12*ε, etc.

>>8412199
bump

>>8414462
x/|x| is ±1.

For integration, you'd normally split the interval into the subintervals where x has a fixed sign, so that |x| can be replaced by either x or -x, and sum them.

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Would it be correct in layman's terms to say that the strong and weak forces are responsible for forming and destroying atoms? Or is that an oversimplification?

Also what is the difference between the strong/weak FORCE and the strong/weak INTERACTION?

Just need a wee bit of help on this

We have [math] \mathcal{U}= \{ X \in \wp ( \mathbb{N} ) | X\,is\,finite \} [/math].

Let [math]f: \mathbb{N} \longrightarrow \wp ( \mathbb{N} ) [/math] be the mapping such that [math] x \neq y \Rightarrow x \in f(y)\,or\,y \in f(x) [/math].

Show that there's an element in [math] \mathcal{U} [/math] that's of cardinality greater than 100.

>the function assigns to each positive integer its largest decimal digit

Domain is Z+ obviously

But the Range I don't get. Integers can't have decimal digits so it has to be 0

If the domain is any positive integer then range can be any number 1-9.

Which is it? Does range depend on domain? if so it's 0

if Domain is independent then domain can be any number 1-9?

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How do I do this? I see that you can put those two pieces together to make a whole square, but how the fuck do you make the entire shape a square?

>>8414784
"decimal digit" is not digit after decimal point. It's "digit in decimal system" i. e. "digit in base 10"

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>>8414803
something similar to pic related?

>>8414804
wow I'm fucking dumb thank you for not ripping me a new asshole

I feel like I'm either being very pedantic or very retarded.

How do I prove that a derivative exists?

For example, is saying that "if x^2 is differentiable, then its derivative is 2x" proof that x^2 is in fact differentiable? My current problem is a less dumb version of that.

>>8414817
I'm pretty sure any function that is continuous is differentiable. Just state that x^2 has no holes or jumps and that should be that.

>>8414825
>I'm pretty sure any function that is continuous is differentiable.
Underaged detected.

In case you really don't know, |x| is the classic example of "continuous but not differentiable" (consider x=0).

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For the boxed questions, I got that
d. E is 1/5 of its original size
e. E is 5 times its original size
But I don't know how to explain the why. I've used proportionality symbols in my explanation.
d. E ∝ 1/ε -> E is 1/5 its original size when ε = 5 compared to ε = 1 (for air)
e. ½(CV^2) -> ½((5area^2)/d)V^2 -> E ∝ ε -> E is 5 times its original size when ε = 5

Have I explained these thoroughly enough or is there something else I need to say? Feels like I'm waffling.

>>8414817
Just look at f(y)-f(x)/(y-x). If that expression has a limit in y->x, then f is differentiable in x, and its derivative in x is that limit.
e.g. f(x)=x^2
(y^2-x^2) = (y-x)(y+x)
so (y^2-x^2)/(y-x) = (y+x) -> 2*x as y -> x

>>8414612

Pls respond

>>8414817
Yes, if you are able to prove that 2x is indeed the derivative of x^2, then it trivially follows that x^2 has a derivative.

Your figure takes 5 squares, so you want your square to be of side [math]\sqrt{5}[/math].
Luckily the diagonal cut on the side is already [math]\sqrt{2^2+1^2}=\sqrt{5}[/math], so you'll want to make more like this.
Assuming (0,0) to be the bottom left corner, and graduations to be given by the squares with the notation (horizontal#, vertical#),

Cut from (0,1) to (2,2), take the triangle and glue it to the bottom right {what used to be the line ((0,2),(2,2)) to ((1,0),(3,0))}

Cut from (0,1) to (1/2,0), and rotate the small piece around (1/2, 0), you get a square!

Is that vaguely understandable? Explaining geometry is hard.

>>8414773
This is weird. why not just say that [|0,100|] is an element of V and has a cardinality of 101?

>>8414612
It's kind of an oversimplification in the sense that Strong interaction can also be involved in the breaking of an atom. Also, both of these have to do with quarks more than atoms.
Strong interaction makes quarks stick together to form nucleons such as neutrons and protons (among other things). And when they're done, there's still enough strong interaction left to make those nucleons stick to each other. In that sense the first is true, but it does other shit. Same is true for weak interaction.

There's no difference that I know of, but people prefer the term 'interaction' because there is no accurate theory of Weak interaction as a classical notion of force (not sure whether that's also true for strong interaction, but I think so).

>>8414958

Thanks lad

>>8414958

The weak interaction is considered stochastic, no?

In diff eq how does it mathematically make sense to change exp(c) to C? Its something I've come to accept but don't understand.

Hey, mathfags, I've got a question for you.

Who do you think will pay you throughout your life and why?

>>8415095
It doesn't make sense for reals.

>>8415161
*And for complex numbers as well since you can choose C to be 0.

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>>8414888
Is this how you cut it? Because I cant put it together to make a square?

>>8415174
Make the cut on the bottom perpendicular to the cut on the top

>>8415174
>>8414888

nvm I just made my small triangle a bit too big. I see it now. Thanks!

>>8414462
>For example, in the integral sin^2(x)cosx / (sqrt(cos^2(x))
>root
Either u substitution or trigonometric substitution.

>>8415181
Thanks, that makes even more sense. Seriously appreciate it.

>>8415095
its just a relabelling of a constant

its like having a generic quadratic equation
ax^2+bx+c=0

and letting a=2d so that

2dx^2+bx+c=0

>>8412199
>Could someone explain vectors in 2d and/or 3d space?
You can just think of them as arrows that you can "add" by concatenating.
> It also perplexes me that parallelograms can be conveyed using vector coordinates
I don't have any idea what you mean by this.

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Any ideas for this one?

I've been looking at a a 10 by 10 rectangle and trying to think of five different rectangles that would add up to 100. Idk if that's a bad approach or not.

>>8415224
It's bad. You should just look at a square and think of ways you could cut it up.

>>8415228
Mean 10 by 10 square haha. I'll try to just mess with a plain square though. Do you have it figured it out?

how is the energy of an EM wave conserved if it can have larger amplitudes at points about it's propagation distance for z>0?

As in, how can the intensity of the field be larger than it's initial value at some point on z?

>>8415234
Make a center rectangle and then you can divide the outer ring into four rectangles that don't share complete sides with either the center rectangle or each other.

>>8412199
They represent something in different directions.

For example, if you think of temperature, it can only go up and down, it has no direction.
But if you think of say, force, it does, when you apply force to something, you have to chose a direction you're doing that.
The same goes for something like velocity or displacement, you have to choose not only how fast you're going to move, but as well as which direction.

A vector is a mathematical way of representing the directions in independent direction.
So, for example, if you want to go somewhere, you say that's 3 blocks east and 5 blocks north (we can add a 3rd dimension too here, and you can represent that as a vector (3,5)
This vector has a length, which the linear distance between where you are and the place at (3,5) if you were to go on a straight line, this distance is [math]\sqrt{3^2 + 5^2}[/math], from pythagoras theorem (because we chose two directions that are 90º apart, exactly so it would be a triangle rectangle).

You can do the same for 3d vectors, say that the place is on the 4th floor of some building, so you have (3,5,4).

The same way, with say velocity, say you're driving up a mountain at 60km/h, you can brake your velocity in two components for example, how fast you're climbing the mountain (your vertical vecocity) and your horizontal velocity, so you have broken down your velocity into two different components.

Another example, pick a small object and point your index fingers to the object, each other at a 90º angle, so one is pointing from below and the other from the side.
If you push with only one finger, you see the object move in only one direction, say up, if you push with the other you see it moving to the side, to the left or right depending on which finger you chose.
Now if you push with both fingers at the same time, the objects moves diagonally.
That's vector addition, you took two forces that can be broken down in different directions and added them together.

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>>8415243
What exactly do you mean by center rectangle. Something like this?

>>8415264
Yes.

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>>8415266
Woule something like thid be a solution? I think I misunderstood the questuon. At first I thought i meant no rectangles could share the same dimensions? I'm sort of confused what it means noe to be honest.

>>8415277
That works.

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Wouldn't the answer to this question be no? Diagonals of a square are perpendicular and isn't that the most you could get while dissecting a square into triangles?

>>8415221
is this a new meme I'm smelling

>>8414942
sorry, it should be that there exists an integer m such that f(m) is of cardinality greater than 100

but yeah I agree it's a weird problem

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>>8415221

fuck off m8 this shit is impossible

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>>8415221

well fuck me in the ass with a rake, I completely misread this as 5 triangles, which I'm pretty sure is impossible

5 rectangles on the other hand is easy

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>>8415356

Yes

Sorry for the sloppiness but I'm too tired for anything better

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So I was very interested in the autoexplore algorithims that roguelikes use, and tried looking for articles on those or similar things in google scholar, but couldn't find anything.
Basically, anything with the word search in it seems to give me either search based map generation, or actual robotic terrain navigation, which doesn't cover the original thing at all.
Is anybody here enough of a wizard to be able to figure out what I should be searching or point me to a few research papers to read?

I'll post my shitty half-baked map explorer if I get anything decent.

Closest thing to what I want that I've found so far is this:
http://gram.cs.mcgill.ca/papers/chowdhury-16-exhaustive.pdf
I can see a couple of ways this could be adapted to improve what I have, but it relies on the entire map already being known.

>>8414310
if you look at the sailboat in the middle with the flag on it, then at the ball the person in the water is kicking just below and to the right of it.
Then just track directly down to the first striped fence thing.
I think that's wally.

>>8414773
>>8415380
Then what is the point of mentioning U? It seems like there is another mistake in how you wrote the question. Is U the codomain of the function? It should also say "a mapping" not "the mapping."

I'll assume the problem is "Show that there is an x in N such that f(x) is of cardinality > 100." Assume f has this property. For every k, either f(k) is infinite (so we're done) or k is in infinitely many f(x), because [math]f(k) \cup \{x \in \mathbb{N} : k \in f(x)} = \mathbb{N}[/math]. If the domain is U then we are in the latter case anyways.

So, let [math]k_0 = 0[/math], [math]U_0 = f(0)^c, U_{i+1} = U_i \cap f(k_i)^c[/math] and let [math]k_{i + 1} = \min(U_i)[/math]. Notice that U_i is always infinite, and k_0 ... k_i are members of f(x) for every x in U_i+1, so you can get arbitrarily large sets in the image.

>>8415593
That should be [math]f(k) \cup \{x \in \mathbb{N} : k \in f(x)\} = \mathbb{N}[/math]

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>>8415574

here I cleaned it up

>>8414817
> How do I prove that a derivative exists?
From the definition of a derivative:
df(x)/dx = lim[δx->0] (f(x+δx)-f(x))/δx

The derivative exists if if the limit exists, which requires both one-sided limits exist and are equal.

> The limit of f(x) as x approaches p from above is L if, for every ε > 0, there exists a δ > 0 such that |f(x) − L| < ε whenever 0 < x − p < δ. The limit of f(x) as x approaches p from below is L if, for every ε > 0, there exists a δ > 0 such that |f(x) − L| < ε whenever 0 < p − x < δ.

Can I solve the same differential equations with variation of parameters and undetermined coefficients? Are they (always?) interchangeable?

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How do I into this question?

>tfw brainlet
>tfw general relativity is hard

i keep getting different answers when calculating fusion energy output
wikipedia and all other sources i found say that proton boron fusion (H1 + B11 -> 3He4) puts out 8.7MeV
when using the numbers on wikipedia for the mass of the proton, boron11 and helium i get ~11.2MeV
when i calculate joules per kilogram using 8.7MeV i get ~7e14 J/kg
when i use the mass fraction to calculate joules per kilogram though i get ~9e13 J/Kg

i double checked all my math and got the same answers
in case its a problem in the math here's what i did

>11.2MeV per reaction
wikipedia's boron11 mass in unified atomic mass unit
add wikipedia's proton mass in unified atomic mass unit
subtract wikipedia's alpha particle mass 3 times in unified atomic mass unit
convert to MeV

>7e14 J/Kg
mols per kilogram (~12g/mol ~6.022e23)
times reaction energy (8.7MeV)
convert to eV
times google's eV to J conversion

>9e13 J/Kg
same as 11.2MeV except divide by 3 alpha particles' mass
times speed of light squared


what did i do wrong?

>>8415666
The radial distance projected on the flat surface is [math] \displaystyle r = 2a \tan { \frac{180- \lambda }{2}} [/math] and the angle it makes with the x-axis is [math] \phi [/math].
So the x and y projections are [math] x = r \cos{ \phi } [/math] and [math] y = r \sin{ \phi } [/math]

I think you can start by slicing the sphere along different longitudinal planes.

>>8415686
I get 8.7MeV for 1H+11B-3*4He3, or 8.2 MeV replacing the 1H with a proton.

The numbers I'm using are (all from wikipedia):

J/eV = 1.6021766208e-19
kg/u = 1.660539040e-27
c = 299792458 m/s
J/kg = c^2 = 8.9875517873681764e+16
eV/kg = (J/kg) / (J/eV) = 5.60958865e+35
eV/u = (eV/kg) * (kg/u) = 9.31494095e+8

proton = 1.007276466879 u
1H = 1.00782503207 u
11B = 11.0093054 u
4He = 4.00260325415 u
1H+11B = 12.01713043207 u
P+11B = 12.016581866879 u
3*4He = 12.00780976245 u
1H+11B-3*4He = 0.00932066962 u = 8.682 MeV
P+11B-3*4He = 0.008772104429 u = 8.171 MeV

>>8415740
anon you're responding to here
you seem to have the right numbers considering you got the right answer
it seems that there is a difference in mass on different pages (proton v hydrogen and helium v alpha particle)
according to https://en.wikipedia.org/wiki/Alpha_particle
an alpha particle is 4.001506466 which accounts for a difference of 1MeV per alpha particle (thus getting from ~8.2 to ~11.2)
i think the difference is that the isotope page includes the electrons while the particle page does not

so you have solved one of my problems but the other remains

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How do I know which fraction should be inversed? I got it wrong because I flipped the 4/5, not the -2/9.

>>8415780
(a/b) / (c/d) = (a/b)*(d/c)

>>8415782
So only ever flip the second fraction.
Cheers mate

>>8414857
>, then it trivially follows that x^2 has a derivative.
Maybe that's where I'm stuck. I can't see why it's trivial.

>>8415740
>>8415761
same anon again
i found the mistake was the mass fraction i used was skewed by the incorrect number of electrons on either side of the reaction and using the correct numbers i get 6.9708e13 J/Kg

thus this is solved

>>8415761
> an alpha particle is 4.001506466 which accounts for a difference of 1MeV per alpha particle (thus getting from ~8.2 to ~11.2)
Well, the figure for 11B includes 5 electrons, which are 5.4858e-4 u (~0.51 MeV) each, so that's ~2.5 MeV for 5 of them (and also explains why the figure is 0.5 MeV lower for a proton compared to 1H).

>>8414817
>>8414825
>>8414855
>>8414857
>>8415793
>>8415620
Thanks for the help anons, I think I've cracked it, although I had to bust out my old real analysis notes. To (nearly) quote them "we say that f(x) is differentiable if f'(x) exists".

"Exists" simply means "it can be defined in a way that doesn't lead to any contradictions" or more plainly "if I can tell you what it is in non-objectionable terms, it exists".

So
>How do I prove that a derivative exists?
By differentiating your function and not getting something stupid.

> is saying that "if x^2 is differentiable, then its derivative is 2x" proof that x^2 is in fact differentiable?
Well, "we say that f(x) is differentiable if f'(x) exists" and 2x certainly exists so x^2 is in fact differentiable. Basically, in my question I've done it backwards, you should never try to prove something by assuming it's true, assuming that x^2 is differentiable isn't going to prove that it fucking is. It should just be "The derivative of x^2 is 2x, so x^2 is differentiable (and I know that because I've just fucking differentiated it)".

Does that sound right, /sci/?

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What's the difference between Addition and Hydration in reaction mechanisms?
Is hydration just a form of addition?

>>8415884
> "Exists" simply means "it can be defined in a way that doesn't lead to any contradictions" or more plainly "if I can tell you what it is in non-objectionable terms, it exists".
Um, no. There is a fixed definition of what the derivative is. That definition depends upon a function having a limit, i.e. the derivative exists if the limit exists.

> How do I prove that a derivative exists?
By showing that the limit exists.

> Well, "we say that f(x) is differentiable if f'(x) exists" and 2x certainly exists
That's circular reasoning. You can't actually show that 2x is the derivative of x^2 without showing that x^2 is differentiable.

The reason that the derivative of x^2 is 2x is because

lim[δx->0] ((x+δx)^2-x^2)/δx
= lim[δx->0] (x^2+2xδx+δx^2-x^2)/δx
= lim[δx->0] (2xδx+δx^2)/δx
= lim[δx->0] 2x+δx
= 2x

Finding a derivative means finding a limit which means (implicitly) demonstrating the existence of a limit.

For analytic functions, the limit tends to be fairly obvious. In other cases (or if you want a rigorous proof), you need to use the definition of a limit to prove that a particular value is actually a limit.

E.g. in the case of d|x|/dx at x=0, you end up with
lim[δx->0] |δx|/δx
But
lim[δx->0+] |δx|/δx = 1
lim[δx->0-] |δx|/δx = -1

Both one-sided limits exist but are unequal, so the limit doesn't exist, so the derivative doesn't exist

Is there a method of learning a language using logics (lingustics)?

>>8415905
Yes.
t. haisenberg

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A triangle can be cut into three pieces and arranged into a rectangle.

Can anyone explain why this works? I see that this is possible, but how can I understand the reasons why. I see you cut along two midpoints to make a parallelogram.

>>8416006
Read this:
http://users.humboldt.edu/flashman/mdptthrm.html

>>8416006
Look at it like 2 right-angled triangles, you can cut up a right-angled one in 2 pieces to make a rectangle.

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>>8416006

>>8416026
Aw that makes sense. Going to try it with some triangles though.

And this picture sort of is a visual of what this link showed
>>8416032


Thanks guy! More helpful than I ever would have imagined when I asked.

If there's nothing faster than light, how did the dark get there first?

>>8416068
Because there is no information to be sent.

could you give me some hint on how to solve this system?

x^y = y^x
x^2 = y^3

>>8409795
ITT: balls

black balls. white balls.

>>8416095
Is that shit even solvable?

>>8416095
>>8416120
1 is a solution for x and y

>>8416121
yup 1 is obvious
but i think there must be more

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Alright so I see that the area of both squares would be A^2 + B^2 so each side of our new square will have to be the square root of this area.

I have gotten this to work with a 3 x 3 and 4x4 square next to eachother, but can someone show me how it works when the sides will not be a perfect square?

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>>8416130
My attempt

>>8416123
There is. Try using logarithms to get rid of the exponents

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>>8415256
I see, that's a simple yet knowledgable explanation. This helps me a lot, thank you for your time!
>>8415204
Sorry about the bad phrasing on my end! Basically, I have 4 cartesian points of a parallelogram, and one way to solve for the area. I understand it better now. Pic related if my explanation is still badly expressed.

>>8416160
The magnitude of the cross product of two vectors is the product of the magnitudes of the two vectors and the sine of the angle between them.
There's probably a proof of that somewhere in your book.

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How is this even possible?

>>8416130
Unless you're constrained to integer solutions, it doesn't matter whether the sum is a perfect square.

The area will be a^2+b^2 so the side length must be sqrt(a^2+b^2). Note that this is guaranteed to be greater than both a and b, and less than a+b.

Also, >>8416134 isn't a solution because it cuts the shape into four pieces.

>>8416160
Since I never addressed the parallelogram:
The way we can have a vector represent an area is like this:
Imagine you have a plane, now you make a vector perpendicular to the surface, and we make it's magnitude proportional to the area.

But how do we find such a vector?
Well, for a line for example, remember that two points form a a line, but we can also make a vector that is the difference between them, so a single vector forms a line.
Now, two lines form a plane, so two vectors also form a plane.

Conveniently, we have an operation (vector product or cross product) that gives us a vector perpendicular to two other vectors.
So, we can use that to define our area with a vector.

If you imagine two vectors, v and u, with magnitude, say[math]A[/math] and [math]B[/math] that are at a 90º angle to each other, what happens if you draw that?
It looks like two sides of a rectangle.

Now, what's the area of a rectangle? The product of their sides.
But what is the magnitude of the cross product? The product of the length of the vectors, times the sine of the angle between them: [math]||v \times u|| = A B \sin(\theta)[/math]
Since the angle is 90º, sin(90º) = 1

So the magnitude of the cross product is [math]A B[/math], which is exactly the area of a rectangle.
The actual vector [math]v \times u[/math] is a vector perpendicular to this rectangle, so you can actually locate the area in space with just a single vector and know the size of it.

If you change the angle between the vectors you get a parallelogram, and if you look at the formula for the area of a parallelogram, you will find that is exactly the definition of the magnitude of the cross product:
[math]Area = a \cdot h[/math], but what is the height of a parallogram? [math]h = b \sin(\theta)[/math]
[math]Area = a \cdot b \sin(\theta)[/math], which is exactly the magnitude of the cross product, which is also the formula for the area of the parallelogram in terms of the sides.

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Why must it be closed?

>>8416277
f(x) = x has no minimum or maximum on any open interval.

>>8416224
example: divide 5 by 5 square into 25 1 by 1 squares, divide each square of the top row into 4 (0.5x0.5) - get 20 small squares, and 20 bigger squares will be left in the bottom 4 rows. But I'm a brainlet I don't know what principle there is behind such cuts but it's possible you see.

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>>8416130
Here's my solution.

I'm fairly sure that you need to cut it diagonally so that you get sides of the correct length (a^2+b^2=c^2) regardless of a and b.

I have to show this identity holds true:

[eqn]\sum_{n=1}^{+\infty } \frac{2^{-n}}{2n} = ln(2)[/eqn]

It's not a geometric/arithmetic series so I can't find the sequence of partial sums so I can't use the monotone convergence theorem for its sequence of partial sums to show it converges at ln(2). I also can't use the definition of uniform convergence because I don't know the nth term in the sequence of partial sums. Any suggestions?

Is there a method to find the function f(x) to represent another function g(x) as [math]f(x+1)-f(x)[/math]?
Such as for
[math]g(x)=x^2+x[/math] there is [math]f(x)=\frac{1}{3}(x)(x-1)(x+1)[/math]
so [math] f(x+1)-f(x) = g(x) [/math]

>>8416295
Oh I was only thinking of whole units. I'll work on it, but yeah that makes sense.

Thanks bro

>>8416305
What program did you use to make this?

But I was sort of figuring you had to do a diagonal. I think mine was just a special case.

>>8416322
Yes.

>>8416340
fuck yeah dude, thanks! (can you elaborate?)

>>8416352
Wikipedia has many nice formulas to calculate that.

https://en.wikipedia.org/wiki/Indefinite_sum#Definitions

>>8416305
>>8416337
Anyone know how he made these pictures. I'd really like to be able to draw stuff like this for my geometry students. I teach high school.

I've been working through KhanAcademy, and I'm enjoying it; however, I truly want to understand math. KhanAcademy is great in helping me understand simple rules in mathematics, but are there any good intro books to help me better analyze what I'm doing?

I'm working through Algebra II at the moment.

I know this really is a stupid question but it's been so long

If a probability distribution is symmetric about a particular value, is the expectation of the distribution equal to said value?

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>>8416224
Blue squares are 4x4, red are 3x3.

Top/left sides are 3*4+1*3=12+3=15
Bottom/right sides are 3*5=15
Area is 9*((4/15)^2+(3/15)^2)
=9*(16/225+9/225)
=9*25/225
=225/225
=1

>>8416365
Inkscape (SVG editor).

>proofs are hard guise
>you just need to know the definitions and then apply algebra

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How do I make the quotes in LaTeX look normal and not like this?

>>8416392

`` '' -> [math]`` ''[/math]

>>8416393
idgi how do I do that?

>>8416396

`` Hello world ''

look up the csquotes package too

>>8416396
I'm just saying that the stuff on the left are the stuff on the right in latex

>>8416376
> If a probability distribution is symmetric about a particular value, is the expectation of the distribution equal to said value?
Yes.

>>8416405
prove it

fourier sine series for this function:
f(x) = 2hx/L (0<x<L/2)
f(x) = h - 2hx/L (L/2<x<L)
f(x) = 0 elsewhere

how do I set it up?
b_n=(1/L) integral from 0 to L of f(x)sin(n*pi*x)dx?

>>8416407
Shift the distribution horizontally until it's symmetric about the origin.
Now you have an even function.
Multiply that even function by x and you get an odd function. Then, integrating xf(x)dx from -∞ to ∞ is just integrating an odd function over a symmetric interval, and would return zero.

>>8416421
Nice, thanks

>>8416407
If p(m-t)=p(m+t), then:
E[x] = integral[-∞,∞](x*p(x))dx
= integral[-∞,m](x*p(x))dx + integral[m,∞](x*p(x))dx
= integral[-∞,0]((m+t)*p(m+t))dt + integral[0,∞]((m+t)*p(m+t))dt
= integral[0,∞]((m-t)*p(m-t))dt + integral[0,∞]((m+t)*p(m+t))dt
= integral[0,∞]((m-t)*p(m-t) + (m+t)*p(m+t))dt
= integral[0,∞](((m-t) + (m+t))*p(m+t))dt
= integral[0,∞](2*m*p(m+t))dt
= m*(2*integral[0,∞](p(m+t))dt)
= m*(integral[0,∞](p(m+t))dt + integral[0,∞](p(m+t))dt)
= m*(integral[0,∞](p(m-t))dt + integral[0,∞](p(m+t))dt)
= m*(integral[-∞,0](p(m+t))dt + integral[0,∞](p(m+t))dt)
= m*integral[-∞,∞](p(m+t))dt
= m*integral[-∞,∞](p(x))dx
= m

>>8416429
>>8416421
r u a genious

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Last question

>>8416441
>not asking for minimum number of pieces
>not cutting them into 1x1

>>8416418
> fourier sine series for this function:
Fourier series or Fourier transform?

"Series" normally implies that the function is periodic, which means that it can be expressed as the sum of an enumerable (finite or countably-infinite) set of sine waves whose frequencies are integer multiples of the fundamental frequency 2*pi/T, where T is the period.

OTOH, the Fourier transform yields a phase and amplitude for every frequency. For a non-periodic function, the amplitude is "almost never" zero.