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.