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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,730

**This is a brilliant approximation for factorials, particularly, factorials of higher order numbers.For example, 1000! as per this formula is 4.023537292 x 10^2567. The actual value as per the calculator in the scientific mode is 4.0238726 x 10^2567. ** :cool::cool:

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**mikau****Member**- Registered: 2005-08-22
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sweetness!

A logarithm is just a misspelled algorithm.

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**Identity****Member**- Registered: 2007-04-18
- Posts: 934

mikau wrote:

sweetness!

Very much so, if you think an error of

is ok.Offline

**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

I just like how it contains both pi and e.

A logarithm is just a misspelled algorithm.

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**TheDude****Member**- Registered: 2007-10-23
- Posts: 361

Identity wrote:

mikau wrote:sweetness!

Very much so, if you think an error of

is ok.

Which comes out to a relative error of 0.008%. I'll take that.

Wrap it in bacon

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**Daniel123****Member**- Registered: 2007-05-23
- Posts: 663

Identity wrote:

.. not exactly big!mikau wrote:sweetness!

Very much so, if you think an error of

is ok.

EDIT: Aah post collison

*Last edited by Daniel123 (2007-12-11 05:37:01)*

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

depends on what your priorities are i guess.

A logarithm is just a misspelled algorithm.

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**Identity****Member**- Registered: 2007-04-18
- Posts: 934

ganesh wrote:

This is a brilliant approximation for factorials, particularly, factorials of higher order numbers.:cool::cool:

For example, 1000! as per this formula is 4.023537292 x 10^2567. The actual value as per the calculator in the scientific mode is 4.0238726 x 10^2567.

So does this actually converge on the factorial value as n goes to infinity?

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

well both n! and the approximation both diverge to infinity as n goes to infinity

The Beginning Of All Things To End.

The End Of All Things To Come.

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**TheDude****Member**- Registered: 2007-10-23
- Posts: 361

Yes.

http://en.wikipedia.org/wiki/Stirling%27s_approximation

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

i think he meant, does

*Last edited by mikau (2007-12-11 06:36:33)*

A logarithm is just a misspelled algorithm.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I agree that percentage difference is more important than absolute difference.

If you consider the absolute argument the other way, you could say that 10mg of poison on your food is only 10mg more than the recommended amount and so not worth worrying about.

On the same theme, I would guess that this is false:

, but this is true:

Why did the vector cross the road?

It wanted to be normal.

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

isnt that identical? the only time that that would converge to 1, is if the first converged to 0?

The Beginning Of All Things To End.

The End Of All Things To Come.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,630

Because the error may grow, but not as fast as n! grows.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

yeah. Note

but

*Last edited by mikau (2007-12-11 13:20:49)*

A logarithm is just a misspelled algorithm.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

What additional requirement can we impose so that Luca's statement holds?

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Equality? That is, instead of

just getting arbitrarily close to 1, it actually has to get there.Why did the vector cross the road?

It wanted to be normal.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Certainly you can come up with a restriction far less restricting than that. Remember, this restriction can't apply to Mikau's example.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

if the two limits each converge to the same finite number?

*Last edited by mikau (2007-12-12 05:08:17)*

A logarithm is just a misspelled algorithm.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Bingo.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**TheDude****Member**- Registered: 2007-10-23
- Posts: 361

It is also possible for the absolute error to approach 0 while the limits themselves diverge to infinity. As a trivial example, let f(x) = x^2 and g(x) = x^2 + 1/x. Then

and

but

*Last edited by TheDude (2007-12-12 08:09:28)*

Wrap it in bacon

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

Ricky wrote:

Bingo.

awesome! But are there any other restrictions that would do it?

A logarithm is just a misspelled algorithm.

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