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Lemma 1.4.5 If x is an accumulation point of S and ε > 0, then there...

Lemma 1.4.5 If x is an accumulation point of S and ε > 0, then there are an infinite number of points of S within ε of x.

Prove lemma 1.4.5 (Hint: Sippose that for some ε > 0, there were only a finite number of points s1,s2,..,s within ε of x. Let ε' = min{|s1-x|, |s2-x|,... |sn-x|}. Now show that no s exists in S satisfies 0 < |s-x| < ε'.)

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