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Topic: Mathematics as a language
Replies: 35   Last Post: Nov 8, 2010 1:53 AM

 Messages: [ Previous | Next ]
 herb z Posts: 1,187 Registered: 8/26/06
Re: Mathematics as a language
Posted: Nov 4, 2010 2:42 AM

Transfer Principle wrote:
> Herman Jurjus wrote:
> > herbzet wrote:
>
> > > What logically could exist -- that is, what is not inherently self-
> > > contradictory -- has mathematical existence.

> > Corollary: CH is false.
> > Proof: Since Cohen 1963 we know that it is logically consistent to
> > assume that there exists S, subset of P(N), equipollent neither to N nor
> > to P(N).
> > By your principle above, S mathematically exists. Therefore CH is false.

>
> Corollary: CH is true.
> Proof: Since Goedel 1940 we know that it is logically consistent to
> assume that there exists f, a bijection between the set of countable
> ordinals (i.e., aleph_1) and P(N).
> By the principle above, f mathematically exists. Therefore CH is true.
> QED

Mom: Dont enter politics, my son. If you tell the truth men will hate you,
and if you tell lies the gods will hate you. Since you must either tell
the truth or tell lies, you must be hated either by men or by the gods.

Son: I shall do it, mother. For if I tell lies, men will love me for it;
and if I tell truth the gods will love me. Since I must tell truth
or lies, I shall be beloved of men or gods.

--
hz

Date Subject Author
11/2/10 Aatu Koskensilta
11/3/10 herb z
11/3/10 Herman Jurjus
11/3/10 Marshall
11/3/10 Herman Jurjus
11/4/10 herb z
11/4/10 Marshall
11/5/10 herb z
11/5/10 Herman Jurjus
11/6/10 herb z
11/6/10 James Dolan
11/6/10 Tim Little
11/6/10 Daryl McCullough
11/6/10 Marshall
11/6/10 Brian Chandler
11/6/10 Tim Little
11/7/10 lwalke3@lausd.net
11/8/10 Brian Chandler
11/7/10 herb z
11/7/10 Daryl McCullough
11/8/10 herb z
11/3/10 lwalke3@lausd.net
11/3/10 Marshall
11/4/10 herb z
11/4/10 herb z
11/4/10 herb z
11/3/10 Daryl McCullough
11/4/10 Bill Taylor
11/4/10 Daryl McCullough
11/5/10 herb z
11/4/10 herb z
11/4/10 Daryl McCullough
11/5/10 herb z
11/5/10 Daryl McCullough
11/4/10 VK