Some mathematical explorations.
This was when I learned about equivalence relations. I didn't really grok the concept until I thought about it in terms of (what I would learn are called) representatives. I felt strongly that the representative-based presentation is more intuitive, and started to explore it.
For instance, one thing I explore here is constructing Z as follows. Let r : N2 -> N2 take (a, b) and produce (|a - b|, 0) if a > b and (0, |a - b|) otherwise. Then define ~ over N2 as x ~ y iff r(x) = r(y). Then Z = N2/~. This is of course equivalent to the typical construction, but we give preferential treatment to the representative function r over its associated relation ~.