I usually go with "all of the above" rather than "the fanciest." With my six-year-old, I did: - Countable / uncountable infinity (but I didn't go beyond that)

I usually go with "all of the above" rather than "the fanciest." With my six-year-old, I did: - Countable / uncountable infinity (but I didn't go beyond that) - Positive / negative infinity, optionally with NaN - One-point compactification of the real numbers (which is pretty simple -- draw a circle, and map points on the line to the circle) I don't recall if I ever did the one-point of C, but likely I did. The major point, actually, is to understand that there are many ways one can extend numbers, not all compatible with each other, to give bigger sets of numbers. The specifics weren't too important.