elaboration Re: Cantor's Diagonal

The reason it isn't a bijection (of a denumerable set with the set of binary sequences): the pre-image (the left side of your map) isn't a set--you've imposed an ordering. Sets, qua sets, don't have orderings. Orderings are extra. (I'm not a specialist on this stuff but I think Bruno,

Re: Cantor's Diagonal

That isn't a bijection. Barry On Nov 21, 2007, at 10:33 AM, Torgny Tholerus wrote: > Bruno Marchal skrev: >> Le 20-nov.-07, à 23:39, Barry Brent wrote : >>> You're saying that, just because you can *write down* the missing >>> sequence (at the beginning, middle or anywhere else in the list),

Theory of Everything based on E8 by Garrett Lisi

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Re: Cantor's Diagonal

Bruno Marchal skrev: Le 20-nov.-07, à 23:39, Barry Brent wrote : You're saying that, just because you can *write down* the missing sequence (at the beginning, middle or anywhere else in the list), it follows that there *is* no missing sequence. Looks pretty wrong to me. Cant

Re: Cantor's Diagonal

Le 21-nov.-07, à 08:49, Torgny Tholerus a écrit : > meekerdb skrev:Torgny Tholerus wrote: >> >>> >>> An ultrafinitist comment to this: >>> == >>> You can add this complementary sequence to the end of the list. That >>> will make you have a list with this complementary sequence included.

Re: Cantor's Diagonal

Le 20-nov.-07, à 23:39, Barry Brent wrote : > > You're saying that, just because you can *write down* the missing > sequence (at the beginning, middle or anywhere else in the list), it > follows that there *is* no missing sequence. Looks pretty wrong to me. > > Cantor's proof disqualifies any

Re: Cantor's Diagonal

Le 20-nov.-07, à 17:47, David Nyman a écrit : > > On 20/11/2007, Bruno Marchal <[EMAIL PROTECTED]> wrote: > >> David, are you still there? This is a key post, with respect to the >> "Church Thesis" thread. > > Sorry Bruno, do forgive me - we seem destined to be out of synch at > the moment. I'm

Re: Bijections (was OM = SIGMA1)

Le 20-nov.-07, à 17:59, meekerdb a écrit : > > Bruno Marchal wrote: >> . >> >> But infinite ordinals can be different, and still have the same >> cardinality. I have given examples: You can put an infinity of linear >> well founded order on the set N = {0, 1, 2, 3, ...}. > > What is the definiti