TITLE: How many equivalence relations are there on the set $\{1,2,3\}$?
QUESTION [8 upvotes]: How would I do this?
Do I separate it into partitions first? or do I order it by $(1,1)(1,2)(1,3)(2,1)$... etc.

REPLY [12 votes]: There's a one-to-one correspondence between equivalence relations and partitions, so you can certainly do it by carefully writing down all the ways to partition $\lbrace1,2,3\rbrace$ into subsets.