Empty Product - 0 Raised To The 0th Power

0 Raised To The 0th Power

In set theory and combinatorics, the cardinal number nm is the size of the set of functions from a set of size m into a set of size n. If m is positive and n is zero, then there are no such functions, because there are no elements in the latter set to map those of the former set into. Thus 0m = 0 when m is positive. However, if both sets are empty (have size 0), then there is exactly one such function — the empty function. For this reason, authors in combinatorics and set theory frequently define 00 to be 1 when it represents an empty product.