Determine the number of subsets of a set with 7 elements. This would be 128, I believe. Is this correct?

Each subset can be represented by a function f from the set itself, call it $X $, into a $2$ element set ( say $\{0,1\} $), with $f(x)=1$ if $x\in X $ is in the subset and $f (x)=0  $ if not.   Thus we have the function space, $Y^X $, of functions from $X $ to $Y $, known as the power set when $Y $ is a two element set.  Its order is of course  $2^7$, or $2^{|X|}$ in general. ..
