# Contents

## Definition

For $I$ a set, the Kronecker delta-function is the function $I \times I \to \{0,1\}$ which takes the value 0 everywhere except on the diagonal, where it takes the value 1.

Often one writes for elements $i,j \in I$

$\delta^{i}_j \coloneqq \delta(i,j) \,.$

Then

$\delta^i_j = \left\{ \array{ 1 & if i = j \\ 0 & otherwise } \right.$

In constructive mathematics, it is necessary that $I$ have decidable equality; alternatively, one could let the Kronecker delta take values in the lower reals.

## References

Named after Leopold Kronecker.