Gregory Ewing wrote:
Steven D'Aprano wrote:
Fair point. Call it an extension of the Kronecker Delta to the reals
then.
That's called the Dirac delta function, and it's a bit different --
instead of a value of 1, it has an infinitely high spike of zero
width at the origin, whose integral is 1. (Which means it's not
strictly a function, because it's impossible for a true function
on the reals to have those properties.)
You don't normally use it on its own; usually it turns up as part
of an integral. I find it difficult to imagine a numerical algorithm
that relies on directly evaluating it. Such an algorithm would be
numerically unreliable. You just wouldn't do it that way; you'd
find some other way to calculate the integral that avoids evaluating
the delta.
True, but that's the Dirac delta, which as you (and later he) said, is
quite a different thing, not simply a Kronecker delta extended to the
reals. Kronecker deltas are used all the time over the reals; for
instance, in tensor calculus. Just because the return values are either
0 or 1 doesn't mean that their use is incompatible over reals (as
integers are subsets of reals).
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