In the wikipedia page for kronecker delta it says
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?
Best Answer
Math Wikipedia has a lot of small strange mistakes like this, more than I expected; I've corrected several over the last month or two. The Kronecker delta can be defined on an arbitrary set, including the real or the complex numbers but all sorts of others. I'll delete the sentence on Wikipedia.