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Axiom Independence
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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.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131173424
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131173424
- Format Fachbuch
- Titel Axiom Independence
- Herausgeber Betascript Publishing
- Anzahl Seiten 120
- Genre Mathematik
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