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## #26 2011-01-13 21:16:43

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Race with possibility of ties (permutations!)

Wow bobbym, that's awesome!!
Did you derive that, in a day?!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #27 2011-01-13 21:49:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Race with possibility of ties (permutations!)

No, actually the bigger they are the less time it took to derive them. It is the small, compact ones that take years.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #28 2011-01-13 22:33:31

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Race with possibility of ties (permutations!)

Whatever, but I consider it cool!
I don't know such advanced stuffs, so may not be able to understand how you derived it. I have heard only 'Riemann hypothesis', is it the same Riemann in 'Riemann Rearrangement'?
You are a polymath, I am a wannabe

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #29 2011-01-13 22:47:45

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Race with possibility of ties (permutations!)

Hi gAr;

You are a polymath, I am a wannabe

Hope nobody sees that. I think you are overestimating me.

A long time ago Riemann proved that certain series could be rearranged to sum to any value you want. It is called the Riemann Rearrangement theorem. Now Riemann had a knack for never doing anything useful so he is greatly admired by mathematicians. Anyway, some numerical analysts discovered that using his theorem that you could speed up the convergence of slowly converging alternating series by rearranging them.
The effect is quite amazing when it works. In this case I used it on the equation rather than the numbers.

This where it all starts, incidentally Maple uses this series for it's Stirling numbers of the second kind.

From that many approximations are possible. That is how he got his on that page.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #30 2011-01-13 23:09:27

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Race with possibility of ties (permutations!)

All I can say is you are modest. Maybe I have read your articles/books
Thanks for telling one more new math fact!

Last edited by gAr (2011-01-13 23:11:05)

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #31 2011-01-13 23:20:28

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Race with possibility of ties (permutations!)

Me modest, humbug! Nah, no one has read any of it.

I think the Buddha is giving you good advice.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #32 2011-01-13 23:30:54

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Race with possibility of ties (permutations!)

Me modest, humbug! Nah, no one has read any of it.

This may be false!!

Last edited by gAr (2011-01-13 23:32:33)

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #33 2011-01-14 21:19:29

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Race with possibility of ties (permutations!)

I came across a list of formulas summarised in wolfram's site: http://functions.wolfram.com/IntegerFunctions/StirlingS2/

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #34 2011-01-15 00:44:28

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Race with possibility of ties (permutations!)

Hi gAr;

That site contains many functions. Wolfram is quickly becoming the place to go.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #35 2011-01-15 01:01:07

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Race with possibility of ties (permutations!)

Yes bobbym, really so many of them.
It must be the first place to go to know a function!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #36 2011-01-15 01:23:20

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Race with possibility of ties (permutations!)

Besides from that Wolfram has pages and demonstrations as well as videos.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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