How would a proof by induction to show that $n < 2^n$ for all $n \in ℤ$ be related to showing Cantor's Theorem for finite sets?
I have the proof completed however I don't quite see the relation between the two. I understand that Cantor's Theorem states that the power set of any given set will have a greater cardinality than that of the given set.
All explanations are much appreciated thank you.
If a finite set $S$ has cardinality $n,$ what is the cardinality of the power set of $S$?