Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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1. Let (an) be a bounded real sequence. Let
and
U = {u: (EN) (Vn > N)(an <u)}
L = {l: (3N)(\n > N)(an > l)}.
Prove that sup L and inf U exist and satisfy sup L ≤ inf U.
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Transcribed Image Text:1. Let (an) be a bounded real sequence. Let and U = {u: (EN) (Vn > N)(an <u)} L = {l: (3N)(\n > N)(an > l)}. Prove that sup L and inf U exist and satisfy sup L ≤ inf U.
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