1.Problem Statement:(adsbygoogle = window.adsbygoogle || []).push({});

If O is an open subset of ℝ does there exist a sequence in O that converges to x? Explain.

2.Relevant equations

3. The attempt at a solution

So if I define a open subset of ℝ to be open if for all points x [itex]\in[/itex] O there exists a ε-neighborhood [itex]_{V}[/itex]ε (a) [itex]\subseteq[/itex]O.

Then I would use pointwise convergence to prove that for each n[itex]\in[/itex] N, let fn be a function defined on a set A [itex]\subseteq[/itex] ℝ. The sequence fn of function converges pointwise on A to a function f : A → ℝ if for all x in A the sequence of real numbers fn(x) converges to f(x).

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# Homework Help: Sequence that converges to a point

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