Let A and B be any sets, and let left bracketing bar X right bracketing bar be the cardinal number of a set X. Then cardinal exponentiation is defined by ( left bracketing bar A right bracketing bar )^( left bracketing bar B right bracketing bar ) = left bracketing bar set of all functions from B into A right bracketing bar (Ciesielski 1997, p. 68; Dauben 1990, p. 174; Moore 1982, p. 37; Rubin 1967, p. 275, Suppes 1972, p. 116). It is easy to show that the cardinal number of the power set of A is 2^( left bracketing bar A right bracketing bar ), since left bracketing bar {0, 1} right bracketing bar = 2 and there is a natural bijection between the subsets of A and the functions from A into {0, 1}.

cardinal addition | cardinal multiplication | cardinal number | power set