However there is a valid question over what we should
get back from a computer when we calculate
0 ^{0}. If we are thinking in terms of doing an
exact calculation, then there is no question, there is
an answer we should give and that answer is 1. But if
we are thinking in terms of floating point math, then
what the computer should be designed in terms of is,
I have a number close to 0 raised to the power of
another number close to 0 and I need to give back
something that I know is close to the answer.
In that case the computer should give up because the real
answer might be anywhere between 0 and 1 inclusive.
Therefore of his examples, all of the answers make sense.
The two products which are designed to be working with
floating point extensively (ie Excel and his calculators)
think in terms of roundoff error and decide that they
cannot give a reasonable answer. The remaining products
are all programming tools, dealing with integers, and
are assuming for one reason or another that they are dealing
with an exact integer calculation. So all of them give back
the answer 1.
(OK, I admit it, probably the calculators and Excel were
designed by people who remembered that 0^{0} was
an indeterminate form but have no idea what that really
means. But there are calculational contexts in which
failing to give an answer in that case makes sense.)
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