Definition:Kronecker Delta/Number

Definition
Let $\Gamma$ be a set.

Then $\delta_{\alpha \beta}: \Gamma \times \Gamma \to \set {0, 1}$ is the mapping on the cartesian square of $\Gamma$ defined as:


 * $\forall \tuple {\alpha, \beta} \in \Gamma \times \Gamma: \delta_{\alpha \beta} :=

\begin {cases} 1 & : \alpha = \beta \\ 0 & : \alpha \ne \beta \end {cases}$

This use of $\delta$ is known as the Kronecker delta notation or Kronecker delta convention.