(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known dataCan 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.

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# Homework Help: Proof of uniqueness of limits

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