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4. Let D (d,}neN be a set of real numbers satisfying d,41 2 d, +1 for all ne N. Prove that D is an unbounded subset of IR.

4. Let D (d,}neN be a set of real numbers satisfying d,41 2 d, +1 for all ne N. Prove that D is an unbounded subset of IR.

Advanced Engineering Mathematics
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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Answer question 4 Real Analysis
2. Prove that B= (2" |n e N}CR is an unbounded subset of IR. That is, prove that there does not exist an r eR such that a> 2" for all n e N. 3. Let CCRbe a non-empty bounded sabset of integers (where bounded means C is bounded above and bounded below). Prove that sup C is an integer. 4. Let D {d}neN be a set of real numbers satisfying d,412 d+1 for all neN. Prove that D is an unbounded subset of R.
Transcribed Image Text:2. Prove that B= (2" |n e N}CR is an unbounded subset of IR. That is, prove that there does not exist an r eR such that a> 2" for all n e N. 3. Let CCRbe a non-empty bounded sabset of integers (where bounded means C is bounded above and bounded below). Prove that sup C is an integer. 4. Let D {d}neN be a set of real numbers satisfying d,412 d+1 for all neN. Prove that D is an unbounded subset of R.
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