```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 thatmost persons pass over this inconspicuoussmall detail and consequently tangle themselvesin doubt and contradictions over theirrational; but, by observing the factsemphasized here they would spare themselvesthese problems and would clearly discernthat the irrational number, in virtue ofthe property given to it by the definitionshas just as definite a reality in our mindsas the rational numbers or even the integers,and that one does not even need to gain itthrough a limiting process, but by possessionof it one becomes convinced of the practicabilityand evidence of limiting processes ingeneral."Notice the word DEFINITION in Cantor'sstatement.  That is how LOGIC is appliedin the FOUNDATIONAL STUDY of DEMONSTRATIVESCIENCES.
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