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**Summary:**Definition: If M is a set and p is a point, then p is a limit point of M if every open interval containing p contains a point of M different from p.

Prove: that if H and K are sets and p is a limit point of H ∪ K,then p is a limit point of H or p is a limit point of K

In this proof I have assumed that p is not a limit point of H and went on to state that there exists some open interval S that contains p s.t. no element of H (other than possibly p itself) is in S. Since p is limit point of HUK a member of HUK must exist in (a,b) that member being K.

I am currently trying to prove that p is a limit point of K by letting some open interval V be any open interval containing p so S and V intersect but I can not seem to elaborate on what I have.