This page contains an extensive list of topics, axioms, definitions, and theorems in the topic of number systems. 1. * Natural numbers 2. 1. * Peano axioms 3. 2. * Peano arithmetic 4. 3. 1. * Addition 5. 4. 2. 1. * Identity 6. 5. 3. 2. * Commutative property 7. 6. 4. 3. * Associative property 8. 7. 5. * Multiplication 9. 8. 6. 1. * Distributive property 10. 9. 7. 2. * Identity 11. 10. 8. 3. * Commutative property 12. 11. 9. 4. * Associative property 13. * Integers 14. * Rational numbers 15. * Real numbers 16. 1. * Cauchy sequences