Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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,, I've never read up on them, but he warned us that he did not like the theory. – doppz Mar 12 '14 at 17:36

If you accept well-ordering, then consider X as a well-ordered set and then the functions from X to Y represent sequences of the elements of Y according to the well-ordering of X.

So, if X is the ordinal numbers then the functions represent sequences of elements of Y extending through the ordinals.

At a more mundane level, if X is specifically the positive integers, then the functions are what we would normally understand as infinite sequences of elements of Y.

Well, that's one interpretation.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.