[neonskies]

> Going further R (points on a line) to R^2 (points on a plane) is also the same cardinality. The proofs are over my head but they're out there.

It's just a matter of finding a suitable set of functions. For example, you can try proving |R^2| = |(0, 1) x (0, 1)| = |(0, 1)| = |R| where R stands for reals.The middle equality can be proven using Schröder–Bernstein theorem.

[rtkwe]

I follow the line of the proof but finding those actual steps is where being out of the pure math game for 10 years catches up to me. I went into college on a pure math major but transferred to a CS degree. Only needed about 2 classes extra at the end but was tired of school and a simple BS in mathematics wouldn't get me too much in a generic CS career so I just stopped.