Empty Product - 0 Raised To The 0th Power

0 Raised To The 0th Power

Further information: Exponentiation#Zero to the zero 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.

Read more about this topic:  Empty Product

Famous quotes containing the words raised and/or power:

    “Modern tourist guides have helped raised tourist expectations. And they have provided the natives—from Kaiser Wilhelm down to the villagers of Chichacestenango—with a detailed and itemized list of what is expected of them and when. These are the up-to- date scripts for actors on the tourists’ stage.”
    —Daniel J. Boorstin (b. 1914)

    “With an eye made quiet by the power
    Of harmony, and the deep power of joy,
    We see into the life of things.”
    —William Wordsworth (1770–1850)