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 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

--

Alan Smaill