# Axiomatic System

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

## References

### 2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/axiomatic_system#Properties 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.

### 2002

• (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.