fom
Posts:
1,968
Registered:
12/4/12


Re: A size criterion: a question
Posted:
Jan 6, 2013 3:33 PM


On 1/6/2013 2:22 PM, fom wrote: > 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,
Yep, missed a C
ZFC
> > ================================= > "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 > >

