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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Cardinality: revisited.
Replies: 12   Last Post: Dec 27, 2011 2:26 PM

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fishfry

Posts: 1,368
Registered: 12/6/04
Re: Cardinality: revisited.
Posted: Dec 26, 2011 4:00 PM
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In article
<54284908-07b3-4695-ba16-dbef0ece550b@o9g2000vbc.googlegroups.com>,
Zuhair <zaljohar@gmail.com> wrote:

> I shall re-iterate one of my older definitions of Cardinality:
>
> The cardinality of any set x is the set of all sets that are
> equinumerous to x and hereditarily subnumerous to x.
>

Doesn't this run into the "set of all sets" problem? By your definition,
a cardinal is a proper class, which makes using cardinals technical and
difficult.

That's why the traditional (ZF) approach is to choose a canonical set to
represent each cardinality, rather than using the class of all
bijectively equivalents sets.

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