In article <firstname.lastname@example.org>, email@example.com wrote:
> On Tuesday, 18 June 2013 16:32:51 UTC+2, Julio Di Egidio wrote: > > But I guess this is simply because we are overloading the symbol w. > > > Yes. That's the point why set theory fails.
WM's corrupted version of set theory certainly fails in comparison with any of the standard theories.
In WM's WMytheology, the rationals in their standard order are well-ordered.
In standard theories, the rationals in their standard order are are densely ordered.
These two sorts of ordering are incompatible. > > > To sort it out, maybe something looking like the following would work? > >There is no digit number w. But without a digit > number X you cannot have X digits.
While WM may not be able to have as many digits as there are digit numbers, most others can.
For each number in |N, there is an nth digit with value 3 in the decimal expansion for 1/3.