Axiomatic System

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An Axiomatic System is a formal system composed of an axiom set that can be used in conjunction to logically derive theorems.




  • (Wikipedia, 2017) ⇒ Retrieved:2017-1-19.
    • An axiomatic system is said to be consistent if it lacks contradiction, i.e. the ability to derive both a statement and its denial from the system's axioms.

      In an axiomatic system, an axiom is called independent if it is not a theorem that can be derived from other axioms in the system. A system will be called independent if each of its underlying axioms is independent. Although independence is not a necessary requirement for a system, consistency is.

      An axiomatic system will be called complete if for every statement, either itself or its negation is derivable.



  • (Weber, 2002) ⇒ Keith Weber. (2002). “Beyond proving and explaining: Proofs that justify the use of definitions and axiomatic structures and proofs that illustrate technique." For the learning of mathematics.