Let S be a set of integers defined as follows: 2 ∈ S if n ∈ S, then n2 ∈ S if n ∈ S, then 16n ∈ S if n ∈ S, then n * 2n ∈ S Prove that, ∀x ∈ S, ∃q s.t. q is an integer, and 2q = x.

Let S be a set of integers defined as follows: 2 ∈ S if n ∈ S, then n2 ∈ S if n ∈ S, then 16n ∈ S if n ∈ S, then n * 2n ∈ S Prove that, ∀x ∈ S, ∃q s.t. q is an integer, and 2q = x.

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

Let S be a set of integers defined as follows:

2 ∈ S

if n ∈ S, then n2 ∈ S

if n ∈ S, then 16n ∈ S

if n ∈ S, then n * 2n ∈ S

Prove that, ∀x ∈ S, ∃q s.t. q is an integer, and 2q = x.

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