Axioms of Arithmetic 2

Here is a list of the axioms of Arithmetic as stated by Gottlob Frege.


 * 1) Background Information
 * 2) All Real numbers form an algebraic field
 * 3) Fundamental Operations
 * 4) Addition – resulting in a “sum”
 * 5) Multiplication – resulting in a “product”
 * 6) Axioms of Addition
 * 7) Commutative Law of addition: a + b = b + a
 * 8) Associative Law of Addition : a + (b + c) = (a + b) + c
 * 9) Closure Property: a + b is a Real number.
 * 10) Axioms Derived from Axioms of Addition
 * 11) Additive Identity Property: a + 0 = a
 * 12) Additive Inverse Property: For every “a” there is a “-a” such that “a + (-a) = 0”
 * 13) Axioms of Multiplication
 * 14) Commutative Law of Multiplication: a X b = b X a
 * 15) Associative Law of Multiplication: (a X b) X c = a X (b X c)
 * 16) Closure Property: a X b is a Real number
 * 17) Axioms Derived from Axioms of Multiplication
 * 18) Multiplicative Identity Property: a X 1 = a
 * 19) Multiplicative Inverse Property: For every “a” there is a “1/a” such that “a X 1/a = 1”
 * 20) Distributive Property combining Addition & Multiplication
 * 21) (a + b) X c = a X c + b X c
 * 22) Four Additional Axioms – Real numbers are Ordered
 * 23) Given a & b only one of the conditions is true: “a < b” or “a = b” or “a > b”
 * 24) If a > b & b > c, then a > c
 * 25) Monotonic Property of Addition: If a > b then a + c > b + c
 * 26) Monotonic Property of Multiplication: If a > b & c#0 then a X c > b X c