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


Re: Matheology � 166
Posted:
Nov 30, 2012 4:51 PM


In article <4ba4d56a60bb48fe93327f6d8d51df6e@a15g2000vbf.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> For Dedekind defined infinite sets as those that could be put into one > one correlation with proper subsets of themselves, so the criteria for > 'same number' bifurcate: if any two such infinite sets were numerable, > then while, because of the correlation, their numbers would be the > same, still, because there are items in the one not in the other, > their numbers would be different. Hence such 'sets' are not numerable, > and oneone correlation does not equate with equal numerosity [...] > > [H. Slater: "The Uniform Solution of the Paradoxes" (2004)]
If this is supposed to confound the possibility of ontoone mappings between infinite sets, it fails.
And if "equal numerousity" is not the same as bijectability, it has no meaning at all. 



