Limits

Core Sentence / 核心句

A limit describes what a quantity approaches near an input, independently of whether the function reaches or is defined at that input.

中文理解：极限看的是点附近的趋势，不是只看直接代入；点上有 hole 时，附近仍可能趋向唯一值。

x \to a lim f (x) = L

Formal meaning:

\forall ϵ > 0, \exists δ > 0 : 0 < ∣ x - a ∣ < δ \Rightarrow ∣ f (x) - L ∣ < ϵ

看到 approaches、as $x$ goes to、infinite process、derivative definition，就想到 limit。

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