why does 0 to the power of 0 equal 1?

Question

why does 0 to the power of 0 equal 1?

In: 97

Answer 1

There’s already been some posts describing why defining 0^0 = 1 is convenient in power series, Taylor series or some combinatorics applications.

But there’s also situations where 0^0=0 is more convenient, such as defining the discrete metric or the L^0 ‘norm’ (not really a norm). One such example would be to note that the mean is the number that minimises the squared distance from all the points, and the median minimises the distance from all the points, then the mode would minimise the ‘0-th power’ of the distances from all the points, provided that you define 0^0=0.