I'm having trouble answering the last problem Linear Algebra set. Not looking for a solution, of course, but some pointers would be incredibly helpful.
Given a vector space $F^S$ of all functions from the set $S$ to the field $F$, how do you show that $F^S$ is finite dimensional if and only if the set $S$ is finite?
I'd generally attempt to construct a basis for $F^S$, but I can't wrap my head around creating a list of functions that span $F^S$.