why does 0 to the power of 0 equal 1?
In: 97
When a and b are natural numbers, a^b is defined as the number of functions from a set of size b to a set of size a. There is exactly one function from the empty set to itself, so 0^0 = 1.
(It is also true, but irrelevant, that the function f(x, y) = x^y has an essential discontinuity at (0,0).)
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