proof (1+||x+y||) ≤ (1+||x||)(1+||y||) for all x,y element of R

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.2: Properties Of Matrrix Operations
Problem 68E: Proof Prove properties 2, 3, and 4 of Theorem 2.6.
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proof (1+||x+y||) ≤ (1+||x||)(1+||y||) for all x,y element of R

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i dont get why we take the step to show that ||x||||y||≥0 for all x,y in real numebrs?

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