Date: May 2, 2013 10:03 AM
Author: Alan Smaill
Subject: Re: Matheology § 258
WM <firstname.lastname@example.org> writes:
> On 1 Mai, 23:31, Dan <dan.ms.ch...@gmail.com> wrote:
>> > Yes, that is true. But (and please read this very attentively!):
>> > Cantor's argument requires the existence of the complete sequence
>> > 0.111.... in digits:
>> > You can see this easily here:
>> > The list
>> > 0.0
>> > 0.1
>> > 0.11
>> > 0.111
>> > ...
>> > when replacing 0 by 1 has an anti-diagonal, the FIS of which are
>> > always in the next line. So the anti-diagonal is not different from
>> > all lines, unless it has an infinite sequence of 1's. But, as we just
>> > saw, this is impossible.
>> I see no significant difference between referring to a mathematical
>> object by a formula and referring to it by 'writing it down' .
> But Cantor's argument is invalid, in this special case, unless it can
> produce 0.111... with actually infinitely many 1's, i.e. more than
> every finite number of 1's.
> It does not matter whether 1/9 exists as a fraction or whether it
> exísts in the ternary system as 0.01. In order to differ from every
> entry of my list Cantor's argument needs to produce, digit by digit,
> the infinite sequence. And that does not exist.
Not at all;
you accept that for any naturals n,m, (n/m)^2 =/= 2,
and that because you reason that any particular choice
leads to a contradiction. You do not worry in that situation
that you need to check infinitely many cases.
Just reason in the same way here.
WM has double standards.
> Regards, WM