Mathematics is about generalizing concepts and principles to ever larger domains.
In this case, x^y is defined for all pairs (x, y) of real numbers except (0, 0). The question is what limit is "closer" to the set of outputs in the neighborhood of (0, 0) than any other.
0^x is defined for all x except 0, and same for x^0. We can define 0^0 as the limit of one or the other as x goes to 0. and one is constant and more "stable" than the other, so it is typically taken to be that, i.e. 1.
Up next ... if P(X) = false, what is "P(X) for all X in Ø"?
In this case, x^y is defined for all pairs (x, y) of real numbers except (0, 0). The question is what limit is "closer" to the set of outputs in the neighborhood of (0, 0) than any other.
0^x is defined for all x except 0, and same for x^0. We can define 0^0 as the limit of one or the other as x goes to 0. and one is constant and more "stable" than the other, so it is typically taken to be that, i.e. 1.
Up next ... if P(X) = false, what is "P(X) for all X in Ø"?