fom
Posts:
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12/4/12


Re: A size criterion: a question
Posted:
Jan 6, 2013 3:22 PM


On 1/6/2013 1:35 PM, Zuhair 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.
it appears to be equivalent
from Jech on ZF,
================================= "x = y if there exists a onetoone mapping of X onto Y"
injection + surjection =================================== "x <= y if there is a onetoone mapping of X into Y"
injection, surjection undetermined ==================================== "x < y <> ((x <= y) /\ (x = y))"
injection, no surjection

