0^0

[Ralph Gainey]

Dear Tony,

I think you better give up on gambling...

The whole idea of zero is to have an integer on the number line from which
to start quantifying [or perhaps sequencing]. The concept of the exponent is
merely to provide a symbol indicating primarily that one integer is
multiplied by itself a given integral number of times, although non-integral
values are obviously possible. There is no provision for multiplication by
zero anywhere in the arithmetical language, simply because it is a
meaningless, useless concept.
You might develop something by definition, but first you have to define zero
as a quantity, don't you?

With warm regards,
Ralph Gainey