Foundations of Mathematics

Axiomatic System

What are some well-known axiomatic systems?

One of the most well-known axiomatic systems was developed by the Greek mathematician Euclid (c. 325-c. 270 B.C.E.). He presented 13 books of geometry and other mathematics, titled Elements (or Stoicheion in Greek). Included in these books were theorems about geometry and numbers derived from five postulates about points, lines, circles, and angles, four axioms about equality, and one axiom stating “the whole is greater than the part.” A more modern axiomatic system is the axiomatic set theory, which is based on eight axioms and three undefined terms.


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