I was reading this example from my textbook:
Let $S$ be a set of six positive integers whose maximum is at most $14$. Show that the sums of the elements in all the nonempty subsets of $S$ cannot all be distinct. For each nonempty subset $A$ of $S$ the sum of the elements in A denoted $S$ satisfies: $1 \leq S \leq 9 + 10 + 11 + 12 + 13 + 14 = 69 $
And then there are $2^6 - 1 = 63$ non empty subsets of $S$.
Could somebody please explain me the logic of $63$. How is this being calculated.