Let
and
be any sets, and let be the cardinal number
of a set .
Then cardinal exponentiation is defined by
(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 is , since and there is a natural bijection
between the subsets of and the functions from into .
and 
be any sets, and let 
be the cardinal number
of a set 
.
Then cardinal exponentiation is defined by
is 
, since 
and there is a natural bijection
between the subsets of 
and the functions from 
into 
.
