Re: Cantor's Diagonal

From: Torgny Tholerus <torgny.domain.name.hidden>
Date: Wed, 21 Nov 2007 08:49:03 +0100

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.

But then you can make a new complementary sequence, that is not 
inluded.  But you can then add this new sequence to the end of the 
extended list, and then you have a bijection with this new sequence 
also.  And if you try to make another new sequence, I will add that 
sequence too, and this I will do an infinite number of times.  So you 
will not be able to prove that there is no bijection...
======
What is wrong with this conclusion?
    

You'd have to insert the new sequence in the beginning, as there is no 
"end of the list".

  

Why can't you add something to the end of the list?  In an earlier message Bruno wrote:

"Now omega+1 is the set of all ordinal strictly lesser than omega+1, with the convention above. This gives {0, 1, 2, 3, ... omega} = {0, 1, 2, 3, 4, ....{0, 1, 2, 3, 4, ....}}."

In this sentence he added omega to the end of the list of natural numbers...

--
Torgny

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Received on Wed Nov 21 2007 - 02:49:25 PST