Ancient Mesopotamian units of measurement: Difference between revisions

Revision as of 23:17, 21 January 2014

In number theory, the unit function is a completely multiplicative function on the positive integers defined as:

ε (n) = {\begin{cases} 1, & if n = 1 \\ 0, & if n \neq 1 \end{cases}

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 μ(n)).

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+In [[number theory]], the '''unit function''' is a completely [[multiplicative function]] on the positive integers defined as:
+:<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}}