Properties of the Modulus

Ifandare real numbers then

The modulus ofis defined by:

The modulus function has the properties:

is the distance from 0 to x on the number line.

for allandfor all

for all

for allandfor all

for alland

for alland

for alland all inegers

for allandThis is known as the triangle ineqaulity.

for allandThis is known as backwards form of the triangle ineqaulity.

is the diatance on the real number line betweenand

for anyand