The value of either of these is just going to be a function of the other. What does delta and epsilon even mean? What do they establish?
In: Mathematics
This is going to be a bit hard to explain without maths notation, and Reddit isn’t great for that, but let’s give it a go.
Start with [this page](https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of_limit#Precise_statement_for_real-valued_functions).
> Let *f* be a real-valued function defined on a subset *D* of the real numbers. Let *c* be a limit point of *D* and let *L* be a real number.
Putting that into ELi5ish terms, we have some function f(x), defined for x in D, and we want to see if it has a limit L when x = c. I.e. lim x->c f(x) = L
> We say that lim x→c f(x) = L if for every ε > 0 there exists a δ > 0 such that, for all x ∈ D if 0 <|x−c|< δ, then |f(x)−L|<ε.
So what we are doing here is a kind of challenge. You give me an ε as a target. Given your ε, I have to find a δ so that if our x-values are within δ of c, then f(x) is within ε of L.
The ε is the challenge you give me, the δ is the reply I give back. And if I can find a δ for any ε you give me, I win and the function has a limit.
[This diagram may help a bit](https://en.wikipedia.org/wiki/File:L%C3%ADmite_01.svg). This is for continuity but the same principle applies. You give me an ε. For the function to be continuous I have to find some δ so that while we are within δ of c, f(x) is always within ε of L. No matter how small you make ε, no matter how narrow you make the target area, if I can find a δ so f(x) hits the target area, I win and the function is continuous there. I can find a region around the point where the function is arbitrarily close to L.
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