Axiom Independence

Axiom Independence

Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken

     

бумажная книга



Издательство: Книга по требованию
Дата выхода: июль 2011
ISBN: 978-6-1311-7342-4
Объём: 120 страниц
Масса: 203 г
Размеры(В x Ш x Т), см: 23 x 16 x 1

High Quality Content by WIKIPEDIA articles! An axiom P is independent if there is no other axiom Q such that Q implies P. In many cases independency is desired, either to reach the conclusion of a reduced set of axioms, or to be able to replace an independent axiom to create a more concise system (for example, the parallel postulate is independent of Euclid's Axioms, and can provide interesting results when a negated or manipulated form of the postulate is put into its place). Proving independence is usually a simple logical task. If we are trying to prove an axiom Q independent, then the set of all the other axioms P can't imply Q. One way of doing this is by proving that the negation of the set of axioms P implies Q, it then follows by the law of contradiction that P can't imply Q, because if that were the case then P and not P would both imply Q, and that would be a logical contradiction.

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.