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Topic: Matheology � 233
Replies: 37   Last Post: May 12, 2014 10:24 AM

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fom

Posts: 1,968
Registered: 12/4/12
Re: Matheology § 233
Posted: Apr 1, 2013 11:12 AM
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On 4/1/2013 4:51 AM, WM wrote:
> On 31 Mrz., 19:15, Virgil <vir...@ligriv.com> wrote:
>

>>>>> This was the question: In a list containing every rational: Is there
>>>>> always, i.e., up to every digit, an infinite set of paths (rational
>>>>> numbers) identical with the anti-diagonal? Yes or no?

>>
>>>> This is an equally valid question: What's the difference between a duck?
>>
>>> From the standpoint of matheology, perhaps.
>>
>> From the standpoint of logic and common sense, undoubtdly.
>>
>> Your question makes no sense

>
>>
>>> Did you hitherto respond
>>> in an unreasonable way because you misunderstood the question?

>>
>> Your questions assume conditions contrary to fact.

>
> You do not believe that a sequence or list of all rational numbers can
> be constructed? Or do you not believe that the first n digits of all
> these numbers in decimal representation can be compared with the first
> n digits of the anti-diagonal number? Or is there something else you
> do not understand?
>


These questions are not equivalent to the senseless
question above.

Even so, these questions are also senseless because
belief has nothing to do with it.

Then there is...

> As explained before:
>

> > But note that the question also demonstrates WM's
> > complete lack of understanding of the diagonal
> > argument.
> >
> > He has been told time and time again that it is
> > an argument scheme which only has application
> > under certain assumptions.
> >
> > He chooses to believe otherwise for the agenda
> > of his fanaticism.
> >
> > Suppose one is given a countable listing of
> > the rationals (with the appropriate restriction
> > on double representation) according to the
> > infinite listing of an expansion.
> >
> > Suppose one performs a diagonalization on
> > that listing.
> >
> > Is the resultant a rational number? No.
> >
> > What may be concluded? That the rational numbers
> > do not exhaust the capacity of the algorithm
> > to generate representations if that algorithm
> > is to generate a representation for every
> > rational number.
> >
> > Although the burden of proof lies with WM
> > concerning the nature of the diagonal, it
> > is a simple matter to understand if one
> > uses a Baire space representation instead.
> >
> > In the Baire space, rationals are in correspondence
> > with eventually constant sequences. Since,
> > by construction, a list of Baire space rationals
> > would exhaust all of the eventually constant
> > sequences, the resultant of a diagonal argument
> > could not have an eventually constant sequence
> > unless the original premise had been false.










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