Postby **Pfhorrest** » Fri Mar 29, 2019 7:53 pm UTC

There doesn't seem to be a miscellaneous math questions thread, or else I'm blind, so I'm putting this here.

Can the complex numbers be put in 1:1 correspondence with the reals? It seems like two-dimensional numbers built out of integers could be put into correspondence with the naturals (start with 0,0, 1,0, 1,1, 0,1, -1,1, -1,0, -1,-1, 0,-1, 1,-1, then 2,-1, 2,0, 2,1, and so on round and round forever) which can trivially be put in 1:1 correspondence with the integers, so it seems plausible that the complex numbers, being basically two-dimensional reals, might be put in 1:1 correspondence with the reals, but I don't know if the density of the real numbers throws some kind of wrench in that. Something something space-filling curves maybe?