
Re: A size criterion: a question
Posted:
Jan 6, 2013 3:07 PM


On Jan 6, 1:35 pm, Zuhair <zaljo...@gmail.com> wrote: > If we characterize cardinality in the following manner, How much that > would differ from the known cardinality: > > x < y iff there exist an injection from x to y and there do not > exist a surjection from a subset of x to y. > > x > y iff there exist a surjection from a subset of x to y and > there do not exist an injection from x to y. > > x = y iff there exist an injection from x to y and there exist a > surjection from a subset of x to y.
In ZFC there is no difference at all. In ZF there are some striking differences: under your definition, (1) x > y does not imply y < x; (2) x = y does not imply y = x.

