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Let D ⊆ R, a ∈ D, let f, g : D −→ R be continuous...

Let D ⊆ R, a ∈ D, let f, g : D −→ R be continuous functions. If limx→a f(x) = f(a) and limx→a g(x) = g(a) with f(a) < g(a), then there exists δ > 0 such that x ∈ D, 0 < |x − a| < δ =⇒ f(x) < g(x).

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