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


Re: Joel David Hamkins on definable real numbers in analysis
Posted:
Jun 26, 2013 7:17 PM


In article <9254270c601b49a3a979d5d46afa1d31@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Wednesday, 26 June 2013 17:48:25 UTC+2, dull...@sprynet.com wrote: > > > >For all n exists k: >d_1, d_2, d_3, ..., d_n = q_k1, q_k2, q_k3, ..., > > > >q_kn. >This theorem it is not less important than Cantor's theorem: For > > > >all >k: d =/= q_k. > >Both theorems contradict each other. > > > Erm, no they don't. If your "for every n there exists k such that" was > > instead "there exists k such that for every n" then they would contradict > > each other. > > That is the old nonsense with men and women or forks and knifes.
Outside of WM's mytheology, the logical import of "for all x, there is a y such that f(x,y) differ from " "there is a y such that for all x, f(x,y)
Suppose that x and y are members of N, or Z, or Q or R, or any linearly ordered set at all 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!!! See above!!!!! 

