Answered: Let n E N. Prove that if |n − 1| + |n +…

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Let n E N. Prove that if |n − 1| + |n + 1| ≤ 1, then |n² − 1| ≤ 4.

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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Question

I have the following statement which is to be proven trivially or vacuously,

I attempted to prove it vacuously by looking at |n-1|+|n+1|≤1, further simplifying this we get |2n|≤1, which for any natural integer is false {taking into account that 0 does not count in the natural numbers}. Is this the right approach?, my book says this is trivial, Im just really puzzled here.

Let n € N. Prove that if |n − 1| + |n + 1| ≤ 1, then |n² − 1| ≤ 4.

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