Date: Feb 7, 2013 2:15 AM
Author: fom
Subject: Re: More WMythology
On 2/7/2013 12:45 AM, WM wrote:

> Matheology ยง 222 Back to the roots

>

> Consider a Cantor-list with entries a_n and anti-diagonal d:

>

> 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's the origin of matheology.

>

> Regards, WM

>

Correction. That is the origin of WMythology.

"I justify with the observation that

most persons pass over this inconspicuous

small detail and consequently tangle themselves

in doubt and contradictions over the

irrational; but, by observing the facts

emphasized here they would spare themselves

these problems and would clearly discern

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. That is how LOGIC is applied

in the FOUNDATIONAL STUDY of DEMONSTRATIVE

SCIENCES.