# 单侧极限　`def.function-limit-onesided`
左极限与右极限（One-Sided Limits）
layer 15 · 定义 · 实数与极限 · 分析学
[在星图里打开](../#n=def.function-limit-onesided)　·　[节点索引](../index.md)

**左极限** $\lim_{x \to x_0^{-}} f(x) = L$ 指

$$\forall \varepsilon > 0,\ \exists \delta > 0 :\ x_0 - \delta < x < x_0 \implies |f(x) - L| < \varepsilon$$

**右极限** $\lim_{x \to x_0^{+}} f(x) = L$ 把条件换成 $x_0 < x < x_0 + \delta$。
> 陈述续见 [nodes/def.function-limit-onesided.2.md](./def.function-limit-onesided.2.md)


## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/def.function-limit-onesided.3.md](./def.function-limit-onesided.3.md)

refs: Rudin, Principles of Mathematical Analysis, Ch. 4

> 说明见 `notes/def.function-limit-onesided.md`

引用：`def.function-limit-onesided`（内容 v0.9.1）· CC BY 4.0 [LICENSE.txt](../LICENSE.txt)