1. The problem statement, all variables and given/known data Can anyone help me with proving the uniqueness of a limit? The one that stated that a limit, L, only exists if the left and right hand limits at that point are the same? 2. Relevant equations 3. The attempt at a solution I started by saying that let us say a function f(x) has two limits, L1 and L2 at the point a, such that L1<L2, and there exists for both the same epsilon and delta. As x →a-, lim x→a of f(x)= L1, Such that |f(x)-L1|<epsilon , which implies 0<|x-a|<delta ………..(1) Then as x →a+, lim x→a of f(x)=L2 Such that |f(x)-L2|<epsilon, which implies 0<|x-a|<delta ……….(2) By subtracting the epsilon statements from each other, I am left with: 0<L1-L2<0, which is a contradiction, hence L1 and L2 must be the same. I don't know if this is a correct method of proving this, so I would greatly appreciate feedback. If there are any other methods, I would greatly appreciate it. Sorry I couldn't use all the proper mathematical symbols.