Question

Prove the triangle inequality: Given two real numbers x and y, |x| + |y| ≥ |x + y|, where |x| denotes the absolute value of x which equals x when x ≥ 0, and -x when x < 0. Indicate the type of proof you use.

Name: prove the triangle inequality given two real numbers x and y xyxy where x denotes the absolute value of x which equals x when x0 and x when x0 indicate the type of proof you use 25309
Uploaded: 2022-09-21T07:06:19-08:00
Duration: 3 min 32 s
Channel: Ben Blakesley
Description: prove the triangle inequality given two real numbers x and y xyxy where x denotes the absolute value of x which equals x when x0 and x when x0 indicate the type of proof you use 25309

          Prove the triangle inequality: Given two real numbers x and y, |x| + |y| ≥ |x + y|, where |x| denotes the absolute value of x which equals x when x ≥ 0, and -x when x < 0. Indicate the type of proof you use.

Added by Kristin H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ben Blakesley

09/21/2022

Step 1

e., |x| = max(x, -x). ** Show more…

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Prove the triangle inequality: Given two real numbers x and y, |x| + |y| ≥ |x + y|, where |x| denotes the absolute value of x which equals x when x ≥ 0, and -x when x < 0. Indicate the type of proof you use.