Originally Posted by

**tonio** It would really be interesting to know what grad school did Plato attend since they obviously do not abide by ZFC and usual set theory rules. Not taking into consideration the empty set as a set (if this is what Plato really meant) has rather far-reaching consequences in some definite areas in maths (for example, in combinatorics).

Anyway, and going back to the OP question: if $\displaystyle A\,\,\,or\,\,\,B=\emptyset$ , then $\displaystyle A\times B=\emptyset$ and thus there's one unique function from or to the empty set.

As for $\displaystyle 0^0=1$ : it certainly isn't defined but $\displaystyle x^x\xrightarrow [x\to 0^+]{}1$ , so one can safely define $\displaystyle 0^0=1$ as long as we restrict ourselves to positive reals.

Tonio