```Date: May 2, 2013 10:03 AM
Author: Alan Smaill
Subject: Re: Matheology § 258

WM <mueckenh@rz.fh-augsburg.de> 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 choiceleads to a contradiction.  You do not worry in that situationthat you need to check infinitely many cases.Just reason in the same way here.WM has double standards.> Regards, WM-- Alan Smaill
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