Distributive, Identity and Inverse Axioms
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