8 Feb
2009
8 Feb
'09
2:51 p.m.
On Sat, 7 Feb 2009, Toby Bartels wrote:
Toby was of course referring to the Dedekind reals
Actually, I was trying to keep it open, since different schools of constructivism have different opinions about which are the correct reals (as well as which are equivalent). But nobody uses the binary reals, since they can't subtract them.
Never mind subtraction -- you can't even add them. As I mentioned in my last posting, the question "Is x < 1/2?" is decidable for Vaughan's binary reals, but "Is x < 1/3?" is not (constructively), so the operation of adding 1/6 can't be defined. Peter Johnstone