\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(\mathcal{C}^0([0, 1], \mathbb{R})\) be the \(\mathbb{R}\)-vector space of continuous real functions on \([0, 1]\). Show that \(\mathcal{C}^0([0, 1], \mathbb{R})\) is of infinite dimension.
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.