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Topic: Matheology § 201
Replies: 32   Last Post: Jan 28, 2013 2:26 PM

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 Jesse F. Hughes Posts: 9,776 Registered: 12/6/04
Re: Matheology S 201
Posted: Jan 27, 2013 12:46 PM

WM <mueckenh@rz.fh-augsburg.de> writes:

> On 27 Jan., 17:56, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>> William Hughes <wpihug...@gmail.com> writes:
>> > On Jan 27, 2:33 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>> >> On 27 Jan., 14:12, William Hughes <wpihug...@gmail.com> wrote:
>>
>> >> > On Jan 27, 10:40 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>> >> >  <snip>

>>
>> >> > <... |N contains more than all (finite initial segments)
>>
>> >> > Piffle. |N does not contain more that all FISONS
>> >> > nor has anyone claimed this.

>>
>> >> > the correct statement is
>>
>> >> >   For every initial seqment f, there is an element of |N, n(f)
>> >> >   such that n(f) is not in f.  (note that n(f) may change if you
>> >> > change
>> >> >   f)

>>
>> >> > However,
>>
>> >> >   for ever n(f) there is an initial segment g
>> >> >   such that g contains n(f)

>>
>> >> Of course. But these all are relative definitions. As  I said, it is
>> >> impossible to define infinity absolutely. Same is valid for Cantor's
>> >> diagonal: For every line n, there is an initial segment of the
>> >> diagonal that differs from the first n lines. But that does not imply
>> >> that there is a diagonal that differs from all lines.

>>
>> > It does imply that there is a diagonal that differs
>> > from each line.   We start by noting that if a list L has a finite
>> > definition, so does the antidiagonal of L, call it l.  By induction we
>> > show that l differs from each line of L.

>>
>> Frankly, it seems to me that induction is utterly unnecessary.
>>
>> Once we define the anti-diagonal, it is a triviality to show that it
>> differs from each line of L.
>>
>> A minor point, perhaps.

>
> It the list is complete with respect to all terminating decimals, what
> is possible, then the anti-diagonal cannot differ from all lines at
> finite places.

I wasn't trying to enter a second discussion with you. I just wanted
to raise a minor point with William.

I'd prefer to keep to one conversation at a time with you, so that
we can focus on a single point of contention.

--
Jesse F. Hughes
"Disney has now succeeded in preventing anyone from doing to Mickey
Mouse what Disney did to Quasimodo."
-- Randolph Rackovitz, on Eldred vs. Ashcroft