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by SamReidHughes 2473 days ago
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.

1 comments

Update: it's not counterintuitive any more.