---
title: Unit function
slug: unit-function
qid: Q2919265
snapshot: unit-function-339829-ce13356b13924eaf
content_hash: ce13356b13924eaf9cbc888bb242c879d4a38f16bd1bb6b473965ffe48d95ff4
license: CC BY-SA 4.0
source: https://en.wikipedia.org/w/index.php?oldid=1286454130
tags: [116467647, 20476743, 20477140, 23118434, 23468805, 23603337, 24043274, 29176138]
---

# Unit function

> [!note] Provenance
> Snapshot `unit-function-339829-ce13356b13924eaf` · content root `ce13356b13924eaf…`
> Derived from <https://en.wikipedia.org/w/index.php?oldid=1286454130> · Licensed CC BY-SA 4.0

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 }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 \mu(n) , which generally denotes the Möbius function).

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 }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 \mu(n) , which generally denotes the Möbius function). ==See also== Möbius inversion formula Heaviside step function Kronecker delta ==References==