Real Epiphiny


This week my adviser made an off hand remark saying that ℝ need not be the completion of ℚ; any dense set will do. This is obvious, but profound. I had never thought of ℝ this way. I am now working on a definition of ℝ as the completion of the dyadic rationals. The dyadic rationals are convenient because they are basically arbitrary precision binary floating point numbers.


Russell O’Connor: contact me