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Topic: Bijection Between Complex Numbers and Real Numbers
Replies: 59   Last Post: Feb 24, 2012 7:12 AM

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 David Yen Posts: 630 Registered: 3/1/11
Re: Bijection Between Complex Numbers and Real Numbers
Posted: Feb 20, 2012 12:26 AM

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.

|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!

Date Subject Author
2/19/12 Michael Ejercito
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2/19/12 David R Tribble
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2/20/12 jbriggs444@gmail.com
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2/20/12 David Yen
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2/22/12 Tommy Jensen
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2/23/12 Tommy Jensen
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2/21/12 David Yen
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2/22/12 Richard Tobin
2/22/12 David Yen
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2/23/12 trj
2/23/12 David Yen
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2/20/12 David Yen
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