Date: Feb 28, 2013 5:16 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots
On 28 Feb., 22:29, Virgil <vir...@ligriv.com> wrote:

> > > You think that describing this situation as

> > > "there is a line which contains all FISs

> > > of d"

> > > is sensible.

>

> > Every FIS of d.

>

> In standard languages, including both English and German,

> "not all x" and "not every x" both require existence of an x which is

> not whatever is under discussion.

These languages are not suitable to talk about mathematical infinity.

IN infinite sets "not all x" is a triviality, because "all x" is a

faslity. Even the set "all natural numbers have divisor 1" is wrong,

because there is no thing named "all natural numbers". Every natural

number can be divided by 1 without remainder.

"Every natural number is positive." Correct.

"All natural numbers are positive." False. At least completely

meaningless like "tutum trara is blue".

Regards, WM