Welcome to the list!
When I was a student a friend told me about transfinite induction. While
ordinary induction allows you to generalize from n to n + 1 and thus to a
countable set, transfinite induction enables you to explore the continuum.
He didn't explain how it was done, though. I learned later while following a
functional analyses class.
> I know this one!
> I had a friend who published a magazine called "Zorn" printed on pale
> yellow paper... ;)
> Paddy Leahy