(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In Rosenlicht's Intro to Analysis, there is a proposition (p. 52).

A Cauchy sequence of points in a metric space is bounded.

Proof: For if the sequence is P1, P2, P3, ... and ε is any positive number and N an integer such tat d(Pn, Pm) < ε if n, m > N, then for any fixed m > N the entire sequence is contained in the closed ball of center Pm and radius of max{d(Pm, P1),..., d(Pm, PN), ε}

2. Relevant equations

So I wonder when do I use closed or open ball in the proof? I don't really see any difference. Can anybody shed some light on this matter.

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# Homework Help: Open and closed ball

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