Re: just how many reals are there in aleph_1 ?

From: Mark Nudelman (markn_at_greenwoodsoftware.com)
Date: 02/02/05 

Date: Wed, 2 Feb 2005 14:33:44 -0800

|-|erc wrote:
> Take a small section of a list of reals with infinite expansions.
>
> 0.1457..
> 0.2645..
> 0.3878..
> 0.4444..
>
> The diag is 0.1674..
> There is NO WAY 0.2785.. is on that list! (according to theory)
>
> 0.2785.. is an uncountable real for this list! (I can't believe you
> believe this but anyway)

What in the world do _you_ believe? That 0.2785... _is_ on the list? How
could it be, since it's demonstrably different from every number on the
list?

As for the rest of your post, your point seems to be that there are LOTS of
numbers that aren't on this list. Yes, that's obviously true. Given any
list of reals, there are an (uncountable) infinity of real numbers that
aren't on the list. So what?

--Mark

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