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

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lwalke3@lausd.net

Posts: 2,394
Registered: 8/3/07
Re: Mathematics as a language
Posted: Nov 3, 2010 7:50 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Nov 3, 3:23 am, Herman Jurjus <hjm...@hetnet.nl> wrote:
> On 11/3/2010 6:52 AM, 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

(Note: The above "corollary" stems from an earlier sci.math discussion
regarding the relationship between CH and Pen Maddy's "MAXIMIZE".)


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