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


Re: Cantor's absurdity, once again, why not?
Posted:
Mar 15, 2013 6:57 PM


In article <75abcee9c1f64a3cab7691c2c30405a4@fn10g2000vbb.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 15 Mrz., 20:10, Virgil <vir...@ligriv.com> wrote: > > > It is equally possible to show that the two test sets equal without > > looking at any single member of either. > > OIt is equally possible that the sets are different because non > nameable numbers are difficult to biject to each other.
Bijectabiilty of their , nameable or otherwise, is neither neccessry nor sufficient to establish the set equality of set descriptions. > > > > The set of naturals is the same as the union of the set of even naturals > > and the set of odd naturals, > > Not if there are nonnameable numbers. But no such things exist in ZF or any standard set theory.
> How could one be sure that the > same amount of this stuff is in both sets? In general the second set > contains twice the number as every matheologian knows by heart.
Twice what number? The "number" of members in sets is compared by attempting injections between the sets If one can inject both ways, the sets are of equal size. If only one way, then the domain of that injection is the smaller set. > > > > *********************************************************************** > > > > WM has frequently claimed that a mapping from the set of all infinite > > binary sequences to the set of paths of a CIBT is a linear mapping. > > In order to show that such a mapping is a linear mapping, WM must first > > show > > Everything necessary to show has been shown in Matheology § 226.
Only to WMytheologists, not to mathematicians.
Showing that a mapping is bijective in no way establishes that it must also be a linear mapping, and WM has yet to establish that it is, at least to any but WMytheologists. 



