prove for all x,y in R^n: (1+||x+y||) ≥(1+||x||)/(1+||y||)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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prove for all x,y in R^n: (1+||x+y||) ≥(1+||x||)/(1+||y||)
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when we simplify the right hand side "1 + ||x + y|| ≤ (1 + ||x||)(1 + ||y||)/(1 + ||y||) + ||y||" into "1 + ||x + y|| ≤ (1 + ||x|| + ||y|| + ||x|| ||y||)/(1 + ||y||)" where does the +||y|| go?
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