Theorem 2.18. Suppose that (X, p) is a metric space. Suppose furtherthat ECX. Then the following three statements are equivalent:1. The point c € X is an accumulation point of E.2. For every € > 0, the open ball B(c, e) contains infinitely many pointsof E.3. There exists a sequence (Tn)neN of points in E such that x, cand xc as n → ∞o.

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Theorem 2.18. Suppose that (X, p) is a metric space. Suppose further that ECX. Then the following three statements are equivalent: 1. The point c E X is an accumulation point of E. 2. For every > 0, the open ball B(c, e) contains infinitely many points of E. 3. There exists a sequence (Tn)neN of points in E such that x, c and rc as n → ∞.

Theorem 2.18. Suppose that (X, p) is a metric space. Suppose further that ECX. Then the following three statements are equivalent: 1. The point c E X is an accumulation point of E. 2. For every > 0, the open ball B(c, e) contains infinitely many points of E. 3. There exists a sequence (Tn)neN of points in E such that x, c and rc as n → ∞.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 29E

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