An Axiom is a mathematical statement that is assumed to be true.

• The Distributive Axioms are that x(y + z) = xy + xz and (y + z)x = yx + zx.
  These equations are true for all numbers x, y and z.


• The Additive Identity Axiom states that a number plus zero equals that number.
  x + 0 = x or 0 + x = x


• The Multiplicative Identity Axiom states that a number multiplied by 1 is that number.
  x*1 = x or 1*x = x


• The Additive Inverse Axiom states that the sum of a number and the Additive Inverse of that number is zero. Every real number has a unique additive inverse. Zero is its own additive inverse.
  x + (-x) = 0


• The Multiplicative Inverse Axiom states that the product of a real number and its multiplicative inverse is 1. Every real number has a unique multiplicative inverse. The reciprocal of a nonzero number is the multiplicative inverse of that number. Reciprocal of x is 1/x.
  x * 1/x = 1