fishfry
Posts:
1,368
Registered:
12/6/04


Re: Cardinality: revisited.
Posted:
Dec 26, 2011 4:00 PM


In article <5428490807b34695ba16dbef0ece550b@o9g2000vbc.googlegroups.com>, Zuhair <zaljohar@gmail.com> wrote:
> I shall reiterate 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.

