- #1
Mr Davis 97
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Homework Statement
Prove that the cardinality of ##P(S)## is greater than the cardinality of S, where S is any set.
Homework Equations
The Attempt at a Solution
It would seem that we could simply define ##T: S \rightarrow P(S)## such that ##T(s) = \{s \}##. This is clearly an injection, so ##|S| \le |P(S)|##. That seemed too easy though, so I feel like I am doing something wrong.