[limit point proof]: L(aub)=l(a)ul(b)

[jvt05]

Homework Statement

Let L(X) denote the set of limit points of a set X in R^n. How do I prove that L(AUB)=L(A)UL(B)?

The Attempt at a Solution

I know that I have to prove that both sides are subsets of each other, but I have no clue how to start...

 

[CompuChip]

So the standard form of an argument goes like: let $x \in L(A \cup B)$. Then... what does x satisfy (i.e. what is the definition of a limit point of a set X)?

 

[felper]

Remember that if you want to prove a sets equality, you have to prove both inclusions. En this case, there is a trivial inclusion (which?).