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Topic: 6 QUESTIONS That No LOGICIAN Can Answer!!!!!!
Replies: 15   Last Post: Aug 18, 2012 8:12 AM

 Messages: [ Previous | Next ]
 William Hughes Posts: 1,555 Registered: 12/7/10
Re: 6 QUESTIONS That No LOGICIAN Can Answer!!!!!!
Posted: Aug 17, 2012 10:49 PM

On Aug 17, 11:17 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Aug 18, 9:53 am, William Hughes <wpihug...@gmail.com> wrote:
>
>
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>
>
>
>
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> > On Jul 12, 8:54 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > Q1
> > > What are 2 missing reals from this List using Cantor's method?

>
> > > LIST
> > > 0.100..
> > > 0.000..
> > > 0.001..

>
> > A real that begins 0.010...
> > (also missing from LIST')

>
> > > ..
> > > LIST'
> > > 0.000..    (Old Row 2)
> > > 0.100..    (Old Row 1)
> > > 0.001..
> > > ..

>
> > A real that begins 0.110..
> > (also missing from LIST).

>
> So just by examining
>
>  LIST
>  0.100..
>  0.000..
>  0.001..
>  ..
>
> you can calculate
>
> 0.010..
> 0.110..
>
> are BOTH missing?

Indeed (in the sense that at least two real numbers
one starting .010 and one starting .110 are missing)
>
> [X] stands for NOT X.
>
>  LIST
>  0.[1]00..
>  0.0[0]0..
>  0.00[1]..
>  ..
> ==> 0.010..
>
>  LIST
>  0.1[0]0..
>  0.[0]00..
>  0.00[1]..
>  ..
> ==> 0.110..
>
> because you can flip the first digit (of some row)
> and flip the second digit (of some row)
> (without missing any rows)?
>
> So some real beginning
>
> 0.000...
> 0.001...
> 0.010...
> 0.011...
> 0.100...
> 0.101...
> 0.110...
> 0.111...
>
> are all missing too right?
>

Yes, (although you have not shown this
for all cases, eg. 0.100...)
Note however that there are reals
starting 0.100... 0.000... and 0.001..
that are not missing and are not the antidiagonal
of the main diagonal of any *permutation* of the list.

Date Subject Author
7/12/12 Graham Cooper
8/17/12 William Hughes
8/17/12 Graham Cooper
8/17/12 William Hughes
8/17/12 Graham Cooper
8/17/12 William Hughes
8/17/12 Graham Cooper
8/17/12 William Hughes
8/18/12 Graham Cooper
8/18/12 William Hughes
8/18/12 Graham Cooper
8/18/12 William Hughes
8/17/12 Virgil
8/18/12 Graham Cooper
8/18/12 Virgil
8/17/12 Virgil