>>> Bob Sewell on Infinity 
 WE> A 1-1 function is an invertible function, a bijection.
 BS> Well, try injective.  A bijection is a 1-1 correspondence.
An invertible function or injection is a 1-1 function or bijection.
 
 BS> defined a function F:X->Y as ONTO (or surjective) iff for every y in
 BS> the set Y, there exists an x in the set X | F(x) = y.
Never heard about surjections.  Modern math is too much like modern doctors, 
injecting too much. -)  F:X->Y is onto when the range of F = Y.
 
 BS> I've just been learning it the last year or so in college.
What course?  Set theory?  What college level?  Now 2^A > A for all cardinal 
numbers as proven originally by Cantor.  You yourself claim that demunmerable 
 is greater than the cardinality of the continuum, which is an example of 2^A 
> A.  State your position on this contentious point, that you can prove A^A = 
A, for infinite A as claimed earlier.
How do you prove A = A + A for all infinite A, not just for the infinite 
cardinalities of integers and reals.  Don't remember Cantor's proof tho I 
remember how to prove 2^A > A.  An easier problem is to prove that a set S is 
infinite iff (if and only if) it is equinumerous with a proper subset of 
itself.  Can it be proven without the Axiom of Choice?  BTW, the Axiom of 
Choice is different than the right to choose. -)
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