... >> Mathematics >> General Math Terminology >> Independent
Definition: 1. Describing an axiom of a formal (logical) system that is not a formal consequence of any other axioms. 2. Describing a rule of inference of a formal system that cannot be derived from the axioms and the remaining rules of inference. If an axiom or a rule of inference fails to be independent then the formal system may still be acceptable, even though it may not be economical.
Source: "independent." The Penguin Dictionary of Mathematics. London: Penguin, 2008. Credo Reference. Web. 13 August 2012.