[Dewie]

I guess an example of corecursion is an inductive definition of the natural numbers:

Let N be a set.

1. zero is in N.

2. If an element e is in N, then s(e) is in N.

You get: {zero, s(zero), s(s(zero)),...} (of course in any order, since sets are unordered).

You start from zero and build the whole infinite set from that starting point. Bottom up.