MATH137 Study Guide - Final Guide: Triangle Inequality, Upper And Lower Bounds, Classification Of Discontinuities

Triangle Inequality: We prove Property 5 of absolute values, the triangle inequality:

1. Verify that the triangle inequality holds for and , for and , and for and .

2. Prove that the Triangle Inequality is true for all real numbers and .

PROVE: Triangle Inequality We prove property 5 of absolute values, the triangle Inequality:

(a) Verify that the triangle Inequality holds for x= 2 and y = 3, for x = -2 and y = -3, and for x = -2 and y = 3

(b) Prove that thet triangle inequality is true for all real numbers x and y. [Hint: Take cases]

The set of all points on the real line whose distance from zero is less than 3 can be described by the absolute value inequality ll _____.