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Re: Bijection Between Complex Numbers and Real Numbers
Posted:
Feb 20, 2012 12:26 AM
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Now it's my turn:
P(S) represents the power set of S.
W(S) represents the set of all possible well orderings of S.
How do you prove that there exists a bijection between P(S) and W(S) when S is countably infinite?
Let's define the Wendy numbers as opposed to Beth numbers, where Wendy_(n+1) = (Wendy_n)!.
Can you prove or disprove the new continuum hypothesis:
For all n in N, Wendy_n >= Beth_n >= Aleph_n.
Actually, you can start with an easier one:
|P(P(P(S)))| > |W(P(S))| >= |P(P(S))|
I will give you another cardinal afterwards when the Axiom of Concatenation can be agreed upon.
Best wishes!
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