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Topic: Uncountable Diagonal Problem
Replies: 52   Last Post: Jan 6, 2013 2:43 PM

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ross.finlayson@gmail.com

Posts: 1,207
Registered: 2/15/09
Re: Uncountable Diagonal Problem
Posted: Jan 2, 2013 3:37 AM
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On Jan 1, 11:22 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> <ef09c567-1637-46b8-932a-bcb856e41...@r10g2000pbd.googlegroups.com>,
>  "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>

> > On Jan 1, 8:59 pm, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > > <5e016173-aa1b-4834-9d70-0c6b08f19...@jl13g2000pbb.googlegroups.com>,
> > > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:

>
> > > > On Jan 1, 7:29 pm, Virgil <vir...@ligriv.com> wrote:
> > > > > In article
> > > > > But in that proof Cantor does not require a well ordering of the reals,
> > > > > only an arbitrary sequence of reals which he shown cannot to be all of
> > > > > them, thus no such "counting" or sequence of some reals can be a count
> > > > > or sequnce of all of them.
> > > > > --

>
> > > > Basically
>
> > > Nonsense deleted!
> > > --

>
> > Nonsense deleted, yours?
>
> Nope!
> --



Great: from demurral to denial.

There are uncountably many intervals in the reals, that intersect or
don't, each contains rationals.

In ZFC, how many intervals in the reals are there? Uncountably many.

How many disjoint intervals? Only countably many.

How many nested? Only countably many.

Intervals are disjoint, nested, or intersecting.

Then there are uncountably many intersecting intervals, but their
intersections nest in them and their disjoints are disjoint. For each
intersection there's a nest, and a disjoint.

So, in ZFC, how many intervals in the reals are there? Any two points
define an interval, and in ZFC, there are uncountably many of those.

Disjoint or nested Intervals in the reals inject into the rationals.

Regards,

Ross Finlayson


Date Subject Author
12/30/12
Read Uncountable Diagonal Problem
William Elliot
12/30/12
Read Re: Uncountable Diagonal Problem
Butch Malahide
12/30/12
Read Re: Uncountable Diagonal Problem
Shmuel (Seymour J.) Metz
12/30/12
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
12/30/12
Read Re: Uncountable Diagonal Problem
Virgil
12/30/12
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
12/30/12
Read Re: Uncountable Diagonal Problem
Virgil
12/30/12
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
12/30/12
Read Re: Uncountable Diagonal Problem
Virgil
12/30/12
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
12/31/12
Read Re: Uncountable Diagonal Problem
Virgil
12/31/12
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
12/31/12
Read Re: Uncountable Diagonal Problem
Virgil
12/31/12
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
1/1/13
Read Re: Uncountable Diagonal Problem
Virgil
1/1/13
Read Re: Uncountable Diagonal Problem
Virgil
1/1/13
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
1/1/13
Read Re: Uncountable Diagonal Problem
Virgil
1/1/13
Read Re: Uncountable Diagonal Problem
Virgil
1/1/13
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
1/1/13
Read Re: Uncountable Diagonal Problem
Virgil
1/1/13
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
1/1/13
Read Re: Uncountable Diagonal Problem
Virgil
1/1/13
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
1/1/13
Read Re: Uncountable Diagonal Problem
Virgil
1/2/13
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
1/2/13
Read Re: Uncountable Diagonal Problem
Virgil
1/2/13
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
1/2/13
Read Re: Uncountable Diagonal Problem
Virgil
1/3/13
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
1/3/13
Read Re: Uncountable Diagonal Problem
Virgil
1/3/13
Read Re: Uncountable Diagonal Problem
Virgil
1/3/13
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
1/3/13
Read Re: Uncountable Diagonal Problem: Ross is WRONG, again!
Virgil
1/3/13
Read Re: Uncountably Nested Intervals
ross.finlayson@gmail.com
1/4/13
Read Re: Uncountably Nested Intervals
Virgil
1/4/13
Read Re: Uncountably Nested Intervals
ross.finlayson@gmail.com
1/4/13
Read Re: Uncountably Nested Intervals
fom
1/4/13
Read Re: Uncountably Nested Intervals
ross.finlayson@gmail.com
1/5/13
Read Re: Uncountably Nested Intervals
fom
1/5/13
Read Re: Uncountably Nested Intervals
ross.finlayson@gmail.com
1/5/13
Read Re: Uncountably Nested Intervals
fom
1/6/13
Read Re: Uncountably Nested Intervals
ross.finlayson@gmail.com
1/4/13
Read Re: Uncountably Nested Intervals
Virgil
12/30/12
Read Re: Uncountable Diagonal Problem
forbisgaryg@gmail.com
12/30/12
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
12/31/12
Read Re: Uncountable Diagonal Problem
Virgil
12/31/12
Read Re: Uncountable Diagonal Problem
ross.finlayson@gmail.com
12/31/12
Read Re: Uncountable Diagonal Problem
Virgil
1/1/13
Read Re: Uncountable Diagonal Problem
Graham Cooper
1/1/13
Read Re: Uncountable Diagonal Problem
Virgil
1/1/13
Read Re: Uncountable Diagonal Problem
camgirls@hush.com
12/31/12
Read Re: Uncountable Diagonal Problem
Shmuel (Seymour J.) Metz

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