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*16. Recall that N(s; e) = {x:|x − s| 0 there exists M€ N such that n≥M implies that s, € N(s; e). (b) s,→s iff for each > 0 all but finitely many s, are in N(s; c). (c) s,→s iff, given any open set U with s€ U, all but finitely many s are in U.

*16. Recall that N(s; e) = {x:|x − s| 0 there exists M€ N such that n≥M implies that s, € N(s; e). (b) s,→s iff for each > 0 all but finitely many s, are in N(s; c). (c) s,→s iff, given any open set U with s€ U, all but finitely many s are in U.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...
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*16. Recall that N(s; e) = {x:|x − s|<e) is the neighborhood of s of radius ɛ. Prove the following. (a) s,→s iff for each > 0 there exists M€ N such that n≥M implies that s, € N(s; e). (b) s,→s iff for each > 0 all but finitely many s, are in N(s; c). (c) s,→s iff, given any open set U with s€ U, all but finitely many s are in U.
Transcribed Image Text:*16. Recall that N(s; e) = {x:|x − s|<e) is the neighborhood of s of radius ɛ. Prove the following. (a) s,→s iff for each > 0 there exists M€ N such that n≥M implies that s, € N(s; e). (b) s,→s iff for each > 0 all but finitely many s, are in N(s; c). (c) s,→s iff, given any open set U with s€ U, all but finitely many s are in U.
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