(Squeeze Principle) Suppose f, g, and h are real-valued functions on a neighborhood of a (perhaps not including the point a itself). Suppose f(x) ≤ g(x) ≤ h(x) for all x and limx→a f(x) = l = limx→a h(x). Prove that limx→a g(x) = l. (Hint: Given ε > 0, show that there is δ > 0 so that whenever 0 < ||x - a|| < δ, we have -ε < f(x) - l ≤ g(x) - l ≤ h(x) - l < ε.)
2. The attempt at a solution
I don't understand the definition of a limit with ε and δ. The question confuses me, frankly, and I don't have any idea where I would begin. Could anyone help me understand this?