Virgil
Posts:
7,034
Registered:
1/6/11


Re: A size criterion: a question
Posted:
Jan 7, 2013 4:22 PM


In article <c3420f7621404e9e94aa4dc82f3a8695@n5g2000vbk.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 7 Jan., 19:18, Zuhair <zaljo...@gmail.com> wrote: > > > > In fact, it's consistent with ZF that there are sets x and y such that > > > both x > y and y = x. > > > > True, but not in this extension of ZF! > > > > True, e.g., for indistinguishable reals. > If you can't distinguish them, you cannot prove that they are more > than the rationals. R = Q. > But if you believe that they exists independently as different numbers > (although nobody can prove it), then R > Q. > > Regards, WM
Again, WM is missing the point. Te properties of x > y and y = x depend on the definitions of x > y and y = x, and the definition that Butch and Zuhair re discussing is not the standard one, so that WM again does not know what he is talking abaout 

