Ancient Mesopotamian units of measurement: Difference between revisions

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In [[number theory]], the '''unit function''' is a completely [[multiplicative function]] on the positive integers defined as:
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:<math>\varepsilon(n) = \begin{cases} 1, & \mbox{if }n=1 \\ 0, & \mbox{if }n \neq 1 \end{cases} </math>  
 
It is called the unit function because it is the [[identity element]] for [[Dirichlet convolution]].
 
It may be described as the "[[indicator function]] of 1" within the set of positive integers.  It is also written as ''u''(''n'') (not to be confused with&nbsp;''&mu;''(''n'')).
 
==See also==
* [[Möbius inversion formula]]
* [[Heaviside step function]]
* [[Kronecker delta]]
 
[[Category:Multiplicative functions]]
[[Category:One]]
 
 
{{numtheory-stub}}

Revision as of 16:39, 28 February 2014

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