It seems to me that most high school students are comfortable with the intuitive notion of a limit ("as $x$ gets arbitrarily close to $c$, $f(x)$ gets arbitrarily close to $L$") and gain little insight from learning the $\varepsilon$-$\delta$ definition. Is the added rigor of the $\varepsilon$-$\delta$ definition worth teaching at the high school level?
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