Factorial - Revision history

Vipul: /* Related notions */

2012-07-03T17:58:59Z

Related notions

← Older revision		Revision as of 17:58, 3 July 2012
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	* [[lcm of all numbers so far]]: This is the exponential of the [[second Chebyshev function]] and ''also'' equals the [[groupprops:exponent of a group\|exponent]] of the symmetric group of degree <math>n</math>.		* [[lcm of all numbers so far]]: This is the exponential of the [[second Chebyshev function]] and ''also'' equals the [[groupprops:exponent of a group\|exponent]] of the symmetric group of degree <math>n</math>.
	* [[Maximum product over additive partitions]]		* [[Maximum product over additive partitions]]
	* [[~~Maximum~~ lcm over additive partitions]]		* [[Landau's function]] is the maximum lcm over additive partitions.
	* [[Primorial]] is the product of the first few primes.		* [[Primorial]] is the product of the first few primes.

Vipul: /* Behavior */

2012-07-03T17:52:53Z

Behavior

← Older revision		Revision as of 17:52, 3 July 2012
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	===Initial values===		===Initial values===

	The initial values of <math>k!</math> for <math>k=0,1,2,3,4,\dots</math> are given as: <section begin="list"/>[[1]], [[2]], [[6]], [[24]], [[120]], [[720]], [[5040]], [[40320]], [[362880]] [[Oeis:A000142\|View list on OEIS]]<section end="list"/>		The initial values of <math>k!</math> for <math>k=0,1,2,3,4,\dots</math> are given as: <section begin="list"/>[[1]], [[2]], [[6]], [[24]], [[120]], [[720]], [[5040]], [[40320]], [[362880]], <toggledisplay>3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000</toggledisplay> [[Oeis:A000142\|View list on OEIS]]<section end="list"/>


	==Related notions==		==Related notions==

Vipul at 17:52, 3 July 2012

2012-07-03T17:52:20Z

← Older revision		Revision as of 17:52, 3 July 2012
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	==Behavior==		==Behavior==

	~~{{oeis\|A000142}}~~		===Initial values===

	~~===Initial~~ values===		The initial values of <math>k!</math> for <math>k=0,1,2,3,4,\dots</math> are given as: <section begin="list"/>[[1]], [[2]], [[6]], [[24]], [[120]], [[720]], [[5040]], [[40320]], [[362880]] [[Oeis:A000142\|View list on OEIS]]<section end="list"/>

	~~Here are the values of <math>n!</math> for small <math>n = 0,1,2,3,4,5,6,7</math>: <math>1,1,2,6,24,120,720,5040</math>.~~

	==Related notions==		==Related notions==

Vipul at 20:18, 30 April 2009

2009-04-30T20:18:38Z

← Older revision		Revision as of 20:18, 30 April 2009
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	Let <math>n</math> be a nonnegative integer. The '''factorial''' of <math>n</math>, denoted <math>n!</math>, and read as ''n factorial'', is defined as the product of all the natural numbers from <math>1</math> to <math>n</math>. Note that <math>0!</math> is defined as <math>1</math>.		Let <math>n</math> be a nonnegative integer. The '''factorial''' of <math>n</math>, denoted <math>n!</math>, and read as ''n factorial'', is defined as the product of all the natural numbers from <math>1</math> to <math>n</math>. Note that <math>0!</math> is defined as <math>1</math>.

			<math>n!</math> is also the order of the [[groupprops:symmetric group\|symmetric group]], or the group of ''all'' permutations, on a set of size <math>n</math>.

	==Behavior==		==Behavior==

			{{oeis\|A000142}}

	===Initial values===		===Initial values===
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	==Related notions==		==Related notions==

			* [[lcm of all numbers so far]]: This is the exponential of the [[second Chebyshev function]] and ''also'' equals the [[groupprops:exponent of a group\|exponent]] of the symmetric group of degree <math>n</math>.
			* [[Maximum product over additive partitions]]
			* [[Maximum lcm over additive partitions]]
	* [[Primorial]] is the product of the first few primes.		* [[Primorial]] is the product of the first few primes.

Vipul: Created page with '==Definition== Let $n$ be a nonnegative integer. The '''factorial''' of $n$ , denoted $n!$ , and read as ''n factorial'', is defined as the produc...'

2009-04-30T20:06:04Z

Created page with '==Definition== Let <math>n</math> be a nonnegative integer. The '''factorial''' of <math>n</math>, denoted <math>n!</math>, and read as ''n factorial'', is defined as the produc...'

New page

==Definition==

Let <math>n</math> be a nonnegative integer. The '''factorial''' of <math>n</math>, denoted <math>n!</math>, and read as ''n factorial'', is defined as the product of all the natural numbers from <math>1</math> to <math>n</math>. Note that <math>0!</math> is defined as <math>1</math>.

==Behavior==

===Initial values===

Here are the values of <math>n!</math> for small <math>n = 0,1,2,3,4,5,6,7</math>: <math>1,1,2,6,24,120,720,5040</math>.

==Related notions==

* [[Primorial]] is the product of the first few primes.

Factorial - Revision history

Vipul: /* Related notions */

Vipul: /* Behavior */

Vipul at 17:52, 3 July 2012

Vipul at 20:18, 30 April 2009

Vipul: Created page with '==Definition== Let n be a nonnegative integer. The '''factorial''' of n, denoted n!, and read as ''n factorial'', is defined as the produc...'

Vipul: Created page with '==Definition== Let $n$ be a nonnegative integer. The '''factorial''' of $n$ , denoted $n!$ , and read as ''n factorial'', is defined as the produc...'