Re: Ultimate debunking of Cantor's Theory


"Calvin" <crice5@xxxxxxxxxxxxxx> wrote in message news:1184345067.653792.85560@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Jul 13, 12:08 pm, "Peter Webb"
As you have been very polite, and spent
some time on this, I will give it
another go.
...

This finally dawned on me, while you were making your
new attempt to make me understand:

A countably infinite list of binary expansions of
reals between 0 and 1 can't be shown to fail to have
a diagonal-flip-produced number on the list.

The OP's example, among many others, can be used to
prove this proposition by illustration.

I understand now.

I still quibble with the OP's example, because it is
a list of the same number over and over again. But
that could easily be fixed in a variety of ways. At
first I didn't assume that he meant the same number
over and over again, but now I think he did.


If you really understand, you will see that producing even one such list disproves the requirement that the construction always produces the same number. The example he gave trivially had that property. He produced a list where the diagonal expansion failed to provide a number not on the list, in fact he only had two different numbers on the list and the diagonal number happened to be one of the two. My example was very similar, except I picked a list with an infinite number of different reals. His worked exactly the same, but only needed two different numbers in the list to prove that it isn't a different number; I had an infinite number.

Hence my statement that maybe it was too clever.




.

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