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5. Let {an} be a sequence of real numbers with an infinite number of values. (That is, there is no finite set A such that an € A for all n.) Prove that {an} has a subsequence that is either strictly increasing or strictly decreasing.

5. Let {an} be a sequence of real numbers with an infinite number of values. (That is, there is no finite set A such that an € A for all n.) Prove that {an} has a subsequence that is either strictly increasing or strictly decreasing.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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5. Let {an} be a sequence of real numbers with an infinite number of values. (That is, there is no finite set A such that an EA for all n.) Prove that {an} has a subsequence that is either strictly increasing or strictly decreasing.
Transcribed Image Text:5. Let {an} be a sequence of real numbers with an infinite number of values. (That is, there is no finite set A such that an EA for all n.) Prove that {an} has a subsequence that is either strictly increasing or strictly decreasing.
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