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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?

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    $\begingroup$ 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. $\endgroup$
    – J.G.
    Dec 10, 2020 at 22:09
  • $\begingroup$ The Iverson bracket or 'indicator function' is general enough to encompass complex numbers, $\endgroup$
    – user321120
    Dec 10, 2020 at 22:24

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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.

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