Basic Identities

Definitions:
  • a: Real Number a
  • b: Real Number b
  • c: Real Number c

Additive Identity

a + 0 = a


Additive Inverse

a + (-a) = 0


Associative of Addition

(a + b) + c = a + (b + c)


Commutative of Addition

a + b = b + a


Subtraction

a - b = a + (-b)


Multiplicative Identity

a * 1 = a


Multiplicative Inverse

a * (1/a) = 1 (if a is not 0)


Multiplication times 0

a * 0 = 0


Associative of Multiplication

(a * b) * c = a * (b * c)


Commutative of Multiplication

a * b = b * a


Distributive Law

a(b + c) = ab + ac


Definition of Division

a / b = a(1/b)