\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f : [0, 1] \to \mathbb{R}\) continuous and \(f > 0\) on \([0, 1]\). Show that there exists \(\alpha > 0\) such that \(f \ge \alpha\) on \([0, 1]\).
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