alvindavis99

CIP School in the Phils.

Algebra: Basic Identities

on August 23, 2012

 

English: Unital associative algebra axioms, wr...

English: Unital associative algebra axioms, written as commutative diagrams (Photo credit: Wikipedia)

Closure Property of Addition

Sum (or difference) of 2 real numbers equals a real number

 

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

Definition of Subtraction

a – b = a + (-b)

Closure Property of Multiplication

Product (or quotient if denominator (!=)0) of 2 reals equals a real number

Multiplicative Identity

a * 1 = a

Multiplicative Inverse

a * (1/a) = 1     (a (!=) 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)

 

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