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Prove: If s S6sn for all n EN and if both sn Land un+ L, where LE R, then t - L asn- 0 as well. That is, prove that if e> 0 then there exists NENsuch that n2No t-L

Prove: If s S6sn for all n EN and if both sn Land un+ L, where LE R, then t - L asn- 0 as well. That is, prove that if e> 0 then there exists NENsuch that n2No t-L

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.1: Ideals And Quotient Rings
Problem 19E: 19. Let and be nonzero integers. Prove that if and only if divides .
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A. Prove: If s < t. < ua for all n EN and if both sn - L and u,n+ L, where LE R, then t -Las n o0 as well. That is, prove that if e> 0 then there exists N EN such that It. -LI<e (This is sometimes called the squeeze theorem.)
Transcribed Image Text:A. Prove: If s < t. < ua for all n EN and if both sn - L and u,n+ L, where LE R, then t -Las n o0 as well. That is, prove that if e> 0 then there exists N EN such that It. -LI<e (This is sometimes called the squeeze theorem.)
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