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Topic: Matheology § 166
Replies: 2   Last Post: Nov 30, 2012 8:56 PM

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Virgil

Posts: 7,011
Registered: 1/6/11
Re: Matheology � 166
Posted: Nov 30, 2012 4:51 PM
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In article
<4ba4d56a-60bb-48fe-9332-7f6d8d51df6e@a15g2000vbf.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.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 one-one 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 on-to-one mappings
between infinite sets, it fails.


And if "equal numerousity" is not the same as bijectability, it has no
meaning at all.
--





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