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Author Topic: Mathematics Help Thread  (Read 228968 times)

i2amroy

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Re: Mathematics Help Thread
« Reply #2220 on: September 23, 2016, 06:48:14 pm »

As noted the math basics would be to sum the chances for you getting 2, 3, or 4 sixes respectively. Alternatively in this case you could also do 1 (100%) minus the chance for 1 six happening. Cumulative binomial probabilities like this can very quickly become a whole lot of math; as such if you just need a quick answer (instead of needing this for homework/etc. I find that the calculator at stattrek is pretty useful. Alternatively if you are looking for something aimed more specifically at dice you might check out Anydice.
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MrRoboto75

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Re: Mathematics Help Thread
« Reply #2221 on: September 23, 2016, 09:16:37 pm »

Yeah, you can also work backwards by finding the inverse

Although in that case, remember to find p for 1 six and 0 sixes.
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Reelya

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Re: Mathematics Help Thread
« Reply #2222 on: September 24, 2016, 09:07:48 am »

I found a real-world use for the binomial stuff we were looking at - explaining how FPTP voting disadvantages third-parties as electorate sizes grow bigger. e.g. a third-party won 1/7 of seats in Canada's election. Canada's electorates are about 110000 people each, vs American Congressional Districts, which are about 750000 people each, so they're about 7 times as big. If you view a Congressional District as basically being 7 Canada-electorate sized areas, and assume that winning a majority of those will win you the Congressional seat, you can work out the odds using the binomial equations of winning 4,5,6 or 7 sub-areas out of 7, at odds of 1/7. I get a figure of 1% for that, which is much worse than the result in the smaller regions - winning 14% of them. This shows that high population by itself skews things towards a two-party system with FPTP voting, without needing any special trickery.
« Last Edit: September 24, 2016, 09:13:12 am by Reelya »
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hops

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Re: Mathematics Help Thread
« Reply #2223 on: September 25, 2016, 02:30:03 pm »

How do I solve for the limit as x approaches 0 of cot(2x)cot(pi/2 - x)? I've tried everything, and even the computer can't solve it.
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TheBiggerFish

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Re: Mathematics Help Thread
« Reply #2224 on: September 25, 2016, 02:35:45 pm »

Make sure the problem is right?  If Wolfram has no idea, that's generally a bad sign.
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hops

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Re: Mathematics Help Thread
« Reply #2225 on: September 25, 2016, 02:38:37 pm »

Plugging it into Wolfram, it certainly does have a solution.
It has a solution from graphing the function. I'm trying to solve for it, because I'm a human being that is incapable of making more than ten complex calculations in my head per second.
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Culise

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Re: Mathematics Help Thread
« Reply #2226 on: September 25, 2016, 05:30:42 pm »

Solve it by re-writing it into something considerably easier to solve. Such as something involving tangent.
That's what it sounds like to me as well.

EDIT: Apparently Wolfram Alpha is smart enough to simplify it as well, and it accords with my own simplification as well (albeit with the caveat that WA doesn't make note of particular cases where the original function was undefined, such as at 0 and π/2).  My, but this site is quite nifty; I wish it'd been around when I was taking calc, or even in college.
« Last Edit: September 25, 2016, 05:44:25 pm by Culise »
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Dozebôm Lolumzalìs

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Re: Mathematics Help Thread
« Reply #2227 on: October 04, 2016, 10:00:12 am »

Is this proof decent?

Spoiler: big (click to show/hide)

It's semi-rigorous. That's fine. More rigor is good, but not required. (It's not for an assignment, just a project.)
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MagmaMcFry

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Re: Mathematics Help Thread
« Reply #2228 on: October 04, 2016, 10:23:46 am »

Sorry, but I can't actually find the statement you're trying to prove. Please label your stuff with "Definition", "Lemma", "Claim", "Proof" and such.
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Dozebôm Lolumzalìs

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Re: Mathematics Help Thread
« Reply #2229 on: October 04, 2016, 10:33:20 am »

Oh, geez, I wrote that late at night. Gimme a sec, I'll get it tidied up.
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...Simplification leaves us with the black extra-cosmic gulfs it throws open before our frenzied eyes...
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The only difference between me and a fool is that I know that I know only that I think, therefore I am.
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Helgoland

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Re: Mathematics Help Thread
« Reply #2230 on: October 04, 2016, 11:16:30 am »

Maybe just write straight up tech code. Might be easier to parse.
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Dozebôm Lolumzalìs

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Re: Mathematics Help Thread
« Reply #2231 on: October 04, 2016, 11:22:28 am »

Oops, meant interval instead of set. Thanks for catching that. I got confused because I started talking about the union of two intervals.
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Quote from: King James Programming
...Simplification leaves us with the black extra-cosmic gulfs it throws open before our frenzied eyes...
Quote from: Salvané Descocrates
The only difference between me and a fool is that I know that I know only that I think, therefore I am.
Sigtext!

Dozebôm Lolumzalìs

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Re: Mathematics Help Thread
« Reply #2232 on: October 04, 2016, 11:24:13 am »

Also, "within a sufficiently small region" can be simplified by using open balls.

That's what I was going for, but I didn't know the proper terminology. How would I say "within a sufficiently small region" more concisely?
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Quote from: King James Programming
...Simplification leaves us with the black extra-cosmic gulfs it throws open before our frenzied eyes...
Quote from: Salvané Descocrates
The only difference between me and a fool is that I know that I know only that I think, therefore I am.
Sigtext!

Dozebôm Lolumzalìs

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Re: Mathematics Help Thread
« Reply #2233 on: October 04, 2016, 11:25:03 am »

What domain are we working over here? R? If that's the case, label your "open set (a,b)" an open interval. Makes things a hell of a lot easier to read.

Also, you don't have to label your open intervals in the way you did. Consider subscripts.

No, R is the point that is removed from the domain. Clunky sentence there, I'll fix that.
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Quote from: King James Programming
...Simplification leaves us with the black extra-cosmic gulfs it throws open before our frenzied eyes...
Quote from: Salvané Descocrates
The only difference between me and a fool is that I know that I know only that I think, therefore I am.
Sigtext!

Dozebôm Lolumzalìs

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Re: Mathematics Help Thread
« Reply #2234 on: October 04, 2016, 11:42:09 am »

Ah, THE R. Okay. No, it's not R, it's a (closed? Bounded?) interval.

Wait, I might be misusing domain.

Edit: I meant open, not bounded. That's redundant with closed already included.
« Last Edit: October 04, 2016, 11:55:05 am by Dozebôm Lolumzalìs »
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Quote from: King James Programming
...Simplification leaves us with the black extra-cosmic gulfs it throws open before our frenzied eyes...
Quote from: Salvané Descocrates
The only difference between me and a fool is that I know that I know only that I think, therefore I am.
Sigtext!
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