Bay 12 Games Forum

Please login or register.

Login with username, password and session length
Advanced search  
Pages: 1 ... 168 169 [170]

Author Topic: Mathematics Help Thread  (Read 137942 times)

MaximumZero

  • Bay Watcher
  • Stare into the abyss.
    • View Profile
Re: Mathematics Help Thread
« Reply #2535 on: January 09, 2021, 10:22:59 am »

Y'all don't have to waste time explaining for the benefit of my dumb ass who won't get it. Just carry on and do your thing.
Logged
  
Holy crap, why did I not start watching One Punch Man earlier? This is the best thing.
probably figured an autobiography wouldn't be interesting

bloop_bleep

  • Bay Watcher
    • View Profile
Re: Mathematics Help Thread
« Reply #2536 on: January 15, 2021, 11:52:10 am »

Y'all don't have to waste time explaining for the benefit of my dumb ass who won't get it. Just carry on and do your thing.

You sure? I think you can understand it. Let me know if you want another explanation.

Anyway, I think I have a proof for Van der Waerden's Theorem which can be used to prove that any subset of the positive integers which my professor calls "piecewise synthetic" "piecewise syndetic", which is a set that is the intersection of a set with bounded above gaps between consecutive elements and a set with arbitrarily long runs of consecutive integers, has arithmetic progressions of arbitrarily long length. That was an exercise he gave. I might write it up and I could show it to you guys if you want.

As an example:

Code: [Select]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Syndetic set (gaps bounded above by 3):
X X   X     X X       X        X  X
Thick set (arbitrarily long runs):
X   X X   X X X       X  X  X  X  X
Piecewise syndetic set (intersection of syndetic and thick set):
X     X     X X       X        X  X

EDIT: There is another exercise which is to find a positive upper density subset of the natural numbers that is not piecewise syndetic.
« Last Edit: January 15, 2021, 06:40:22 pm by bloop_bleep »
Logged
Quote from: KittyTac
The closest thing Bay12 has to a flamewar is an argument over philosophy that slowly transitioned to an argument about quantum mechanics.
Quote from: thefriendlyhacker
The trick is to only make predictions semi-seriously.  That way, I don't have a 98% failure rate. I have a 98% sarcasm rate.

MaximumZero

  • Bay Watcher
  • Stare into the abyss.
    • View Profile
Re: Mathematics Help Thread
« Reply #2537 on: January 15, 2021, 06:37:15 pm »

I realize that the post above may have come across as a lot more bitter than I meant it to. Sorry, all. I was trying to be funny and fell flat. But seriously, I'm fascinated with just how much I would have to learn just to be considered semi-literate at these levels. I relish watching the discussion.
Logged
  
Holy crap, why did I not start watching One Punch Man earlier? This is the best thing.
probably figured an autobiography wouldn't be interesting

bloop_bleep

  • Bay Watcher
    • View Profile
Re: Mathematics Help Thread
« Reply #2538 on: January 17, 2021, 01:27:41 pm »

No, it's ok, I understood it was a joke.

Anyway, I've written up a proof of Steinhaus's Theorem using the Lebesgue Density Theorem, though a starting point was given in class. Also, a classmate told me that an example of a positive upper density set that is not piecewise syndetic is the set of square-free integers, which apparently was an example given in class.
Logged
Quote from: KittyTac
The closest thing Bay12 has to a flamewar is an argument over philosophy that slowly transitioned to an argument about quantum mechanics.
Quote from: thefriendlyhacker
The trick is to only make predictions semi-seriously.  That way, I don't have a 98% failure rate. I have a 98% sarcasm rate.

Folly

  • Bay Watcher
  • Steam Profile: 76561197996956175
    • View Profile
Re: Mathematics Help Thread
« Reply #2539 on: February 10, 2021, 11:40:02 pm »

Hey.
I'm not good at mathing...or wording for that matter. But when it comes to mathing, I can usually muddle through just mashing buttons on a calculator and yelling at it until it gives me what what I want.
Since I started messing with Lua a while back(I'm also bad at scripting) I've frequently found myself in situations where I had an iterating value X and needed a correlating value Y which would start at one value and approach another value without ever quite reaching it. Today I finally coaxed a free graphing calculator out of Google and poked at it until it gave me this:



where 'x' is my iterative value, 'b' is the baseline that y is equal to when x is 0, 't' is the upper range that y approaches, and 's' is a scale that shifts the arc up or down as needed.

If anyone has a cleaner or more capable method for what I'm trying to do, I'd love to hear about it. If not, hopefully someone else can get some use out of what I came up with~
Logged

WealthyRadish

  • Bay Watcher
    • View Profile
Re: Mathematics Help Thread
« Reply #2540 on: February 11, 2021, 12:23:16 am »


Bear in mind that for small values of 's' with that function you may end up with errors due to floating point precision.

You might find these functions interesting:

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

A function based on (1-e-x) or (2/pi)atan(x) is probably what I would go for.
« Last Edit: February 11, 2021, 12:35:59 am by WealthyRadish »
Logged

Folly

  • Bay Watcher
  • Steam Profile: 76561197996956175
    • View Profile
Re: Mathematics Help Thread
« Reply #2541 on: February 11, 2021, 01:52:58 am »

Thanks!
With that wiki page I was able to guess at which buttons to mash until my graph got rid of the hole in the middle. I'm not sure how exactly, but that hole probably would have caused problems with something eventually.
Much appreciated!

« Last Edit: February 11, 2021, 02:09:14 am by Folly »
Logged

methylatedspirit

  • Bay Watcher
  • they/them; perpetually lost
    • View Profile
Re: Mathematics Help Thread
« Reply #2542 on: February 15, 2021, 11:28:16 pm »

In my Calculus exam, I completely forgot how to integrate anything that wasn't individual polynomial terms. The exam's over, but I'd figure I'd share these questions because I don't have a damn clue how to solve these and I fear these might eat away at my soul if I continue to not know.


I don't know how to solve these. I have some vague ideas about replacing the complex terms with u, but I forgot the steps that would make that method work. I want a step-by-step solution.
Logged

Vector

  • Bay Watcher
    • View Profile
Re: Mathematics Help Thread
« Reply #2543 on: February 16, 2021, 01:15:54 am »

3cosx - sin^3xcosx

I can integrate 3cosx! it's 3sinx

I can integrate -sin^3xcosx! it was chain ruled. Undo!! -> power was 3! rewind to 4, cosx is chainruling the base sinx, so antiderivative is 1/4*sinx^4

answer: 3sinx-0.25sinx^4 + C


Other one: when I take the derivative of, say, sqrt(x), it becomes (1/2)x^(-1/2). This is a clue for what happens here.

What if the original function was sqrt(3x^2+1)? Then the derivative is (6x/sqrt(3x^2+1))*(1/2).

That is pretty close to what we got in the integrand, it's just that the constant was wrong. We got 3 and we want 2.

So multiply by 2/3 -> the correct integral/antiderivative is (2/3)sqrt(3x^2+1)+C.
« Last Edit: February 16, 2021, 01:18:27 am by Vector »
Logged
nonbinary/genderqueer renegade mathematician and former mafia subforum badass.

don't quote me.

bloop_bleep

  • Bay Watcher
    • View Profile
Re: Mathematics Help Thread
« Reply #2544 on: February 16, 2021, 06:48:06 pm »

Both of those can be done with u-subs. The first one make cos(x) dx into dsin(x), second make 2x dx into dx^2, then that into 1/3 d(3x^2 + 1). Then they're essentially polynomial integrals.
Logged
Quote from: KittyTac
The closest thing Bay12 has to a flamewar is an argument over philosophy that slowly transitioned to an argument about quantum mechanics.
Quote from: thefriendlyhacker
The trick is to only make predictions semi-seriously.  That way, I don't have a 98% failure rate. I have a 98% sarcasm rate.
Pages: 1 ... 168 169 [170]