Difference between revisions of "Factorial"

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(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...')
 
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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>.
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<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==
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{{oeis|A000142}}
  
 
===Initial values===
 
===Initial values===
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==Related notions==
 
==Related notions==
  
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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>.
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* [[Maximum product over additive partitions]]
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* [[Maximum lcm over additive partitions]]
 
* [[Primorial]] is the product of the first few primes.
 
* [[Primorial]] is the product of the first few primes.

Revision as of 20:18, 30 April 2009

Definition

Let be a nonnegative integer. The factorial of , denoted , and read as n factorial, is defined as the product of all the natural numbers from to . Note that is defined as .

is also the order of the symmetric group, or the group of all permutations, on a set of size .

Behavior

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A000142

Initial values

Here are the values of for small : .

Related notions