# Why is the kronecker delta not defined for complex numbers?

The restriction to positive integers is common, but there is no reason it cannot have negative integers as well as positive, or any discrete rational numbers. (...) However, the Kronecker delta is not defined for complex numbers.

This seems completely arbitrary. Why would the kronecker delta not be defined for complex numbers? Defining it over any set $$X$$ as $$\delta: X^2 \to \{0,1\}$$ with $$\delta_{x,y} = 1 \iff x=y$$ seems like a pretty natural generalization.

Is there any reason for it to say in wikipedia that it is not defined for complex numbers?

• The Dirac delta serves much the same role if $X$ is continuous, such as when $X=\Bbb R$ or $X=\Bbb C$, but neither that observation nor any other obvious one explains why $X=\Bbb C$, rather than $X=\Bbb R$, would be singled out in the bizarre excerpt you quoted.
– J.G.
Dec 10, 2020 at 22:09
• The Iverson bracket or 'indicator function' is general enough to encompass complex numbers, Dec 10, 2020 at 22:24