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