Date: Feb 7, 2013 8:22 AM
Author: fom
Subject: Re: Matheology § 222
On 2/7/2013 1:54 AM, WM wrote:

> On 7 Feb., 08:15, fom <fomJ...@nyms.net> wrote:

>> On 2/7/2013 12:45 AM, WM wrote:

>

>>> For every n: (a_n1, a_n2, ..., a_nn) =/= (d_1, d_2, ..., d_n).

>>> For every n: (a_n1, a_n2, ..., a_nn) is terminating.

>>> For every n: (d_1, d_2, ..., d_n) is terminating.

>>

>>> For all n: (a_n1, a_n2, ..., a_nn) =/= (d_1, d_2, ..., d_n).

>>> For all n: (a_n1, a_n2, ..., a_nn) is terminating.

>>> For all n: (d_1, d_2, ..., d_n) is *not* terminating.

>

>> that the irrational number, in virtue of

>> the property given to it by the definitions

>> has just as definite a reality in our minds

>> as the rational numbers or even the integers,

>> and that one does not even need to gain it

>> through a limiting process, but by possession

>> of it one becomes convinced of the practicability

>> and evidence of limiting processes in

>> general."

>>

>> Notice the word DEFINITION in Cantor's

>> statement.

>

> Definition or not - all cases have to be treated similarly:

Sadly, no one is yet properly treating your case.

> "for all"

> either expresses a limit or not.

It does. It is simply not characterized properly

by WMorons

> There is not a bit of logic in

> arbitrary choice.

You mean there is not a bit of logic in

your choices.