|
|
Re: Matheology S 201
Posted:
Jan 27, 2013 11:56 AM
|
|
William Hughes <wpihughes@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.
--
"Sale or rental of this disc is ILLEGAL. If you have rented or
purchased this disc, please call the MPAA at 1-800-NO-COPYS."
-- The MPAA begins a new anti-piracy program,
found on a DVD purchased in China
|
|
