# Is there any interesting interpretation of the set of all functions between two sets?

Is there any way to interpret the set of all functions from a set $X$ to a set $Y$?

There is an interpretation of it as the cartesian product of $X$-many copies of $Y$, but I am asking for a more fun, if you want, interpretation. Maybe something of combinatorial flavour?

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I had a professor who once was telling our class about an idea he had as an undergrad. Since the powerset of $X$ is just all $f:X\to\{0,1\}$ he considered the set of all $f:X\to[0,1]$. They're actually called Fuzzy sets, en.wikipedia.org/wiki/Fuzzy_set, I've never read up on them, but he warned us that he did not like the theory. –  doppz Mar 12 at 17:36