# Question: prove cantors original result for any nonempty set whether finite...

###### Question details

Prove Cantor's original result: for any nonempty set (whether
finite or infinite), the cardinality of S is strictly less than
that of its power set 2^{s}. First show that there is a
one-to-one (but not necessarily onto) map g from S to its power
set. Next assume that there is a one-to-one and onto function f and
show that this assumption leads to a contradiction by defining a
new subset of S that cannot possibly be the image of the map f
(similar to the diagonalization argument).