Question

if an element is added to a closed subset will it still be closed

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Prove: Every finite subset of R is closed

definition of closed: A set A is closed if it contains all it accumulation or limit points.

definition of accumulation point: Let A be a subset of R. A point p∈R is an accumulation or limit point if and only if every open set G containing p contains a point of A different from p.

proof: Let A be a finite subset of R with elements a1,a2,…,an where each ai∈R, i=1,2,…,n.

I am lost where to go from here, I could say that there is an accumulation point in A, but I am confused what I do next.

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