Unit Function
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High Quality Content by WIKIPEDIA articles! In number theory, the unit function is a completely multiplicative function on the positive integers defined as: varepsilon(n) = begin{cases} 1, & mbox{if }n=1 0, & mbox{if }n1 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 (n)). Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular...
High Quality Content by WIKIPEDIA articles! In number theory, the unit function is a completely multiplicative function on the positive integers defined as: varepsilon(n) = begin{cases} 1, & mbox{if }n=1 0, & mbox{if }n1 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 (n)). Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated.
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