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Re: Matheology S 201
Posted:
Jan 27, 2013 12:46 PM
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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
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