- #1
dancergirlie
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Homework Statement
Let x [tex]\in[/tex] R, and let A [tex]\subset[/tex] R. Let (an) be a sequence with an [tex]\in[/tex] A and (an) [tex]\neq[/tex] x for all n [tex]\in[/tex] N, and assume
that x = lim (an.) Prove that x is a limit point of A.
Homework Equations
The Attempt at a Solution
Suppose that x=lim(an). Meaning there exists a N [tex]\in[/tex] N so that for n[tex]\geq[/tex]N:
|an-x|<[tex]\epsilon[/tex]
Which would make the [tex]\epsilon[/tex]- neighborhood of (an)= (an- [tex]\epsilon[/tex], an+ [tex]\epsilon[/tex])
After this I don't know what to do. I need to show that every epsilon neighborhood of V(x) intersects A in some point other than x.
Any tips would be great!