Axiomatic Systems

Abstract

Notice that in the second example, the axioms defined a new term (“identity”). This isn’t an undefined term because the axiom includes a definition. Also, these axioms refer to basic set theory that you learned in Discrete Math. For our purposes, we will assume all of those basic set theory terms are known. It is possible to view set theory itself as another axiomatic system, but that is beyond the scope of this course.