Virgil
Posts:
8,833
Registered:
1/6/11


Re: Joel David Hamkins on definable real numbers in analysis
Posted:
Jun 27, 2013 2:15 PM


In article <dcff0113fff1465fb02596bf50a1335b@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Thursday, 27 June 2013 01:17:19 UTC+2, Virgil wrote: > > > Suppose that x and y are members of N [...] with no maximum member and > > f(x,y) means x < y then "for all x, there is a y such that x < y" is true > > but "there is a y such that for all x, x < y" is false. > > >> In a linear set there is no chance to apply the quantifier trick. > > > Then I have created the impossible!!! > > No, you have just done sober mathematics, probably unconsciously. You cannot > have more than all naturals that have a larger successor.
But one can have the set of all naturals that have a larger successor, which is the set N.
> You cannot have > more than all initial segments (d_1, ..., d_n) of the diagonal.
If there is no complete diagonal, then there is nothing to make those initial segments from. > > Set theorybased mathematics assumes that there is a diagonal d with more > than any natural number of digits d_n.
WM claims his matheological myths prohibit functions with domain N.
Standard mathematics abounds with them.
They are called infinite sequences.
So that in denying the 'diagonal', WM rejects infinite sequences.
> > All (d_1, ..., d_n) is all that you can have of d
See! He did it again! 

