The thing that surprised me yesterday (since I don't know much about topology) is that every metrizable countable set without isolated points is the same. So t

The thing that surprised me yesterday (since I don't know much about topology) is that every metrizable countable set without isolated points is the same. So the numbers k/2^n, the points on the unit circle with rational y/x, or the set Q \ Z, are homeomorphic. The fact that you can slice and dice the rationals is counterintuitive.