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The squeeze theorem is formally stated as follows.
Let I be an interval having the point a as a limit point. Let f, g, and h be functions defined on I, except possibly at a itself. Suppose that for every x in I not equal to a, we have:
g(x) \leq f(x) \leq h(x) \,
and also suppose that:
\lim_{x \to a} g(x) = \lim_{x \to a} h(x) = L. \,
Then \lim_{x \to a} f(x) = L.
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