Abstract The classical “ε-δ” definition of limits is of little use to quantitative purposes, as is needed, for instance, for computational and applied mathematics. Things change whenever a realistic and computable estimate of the function δ(ε) is available. This may be the case for Lipschitz continuous and Hölder continuous functions, or more generally for functions admitting of a modulus of continuity. This, provided that estimates for first derivatives, fractional derivatives, or the modulus of continuity might be obtained. Some examples are given.

中文翻译：

---

关于极限的定量理论：估计收敛速度

摘要 经典的“ε-δ”极限定义对定量目的几乎没有用处，例如计算和应用数学需要。只要函数 δ(ε) 的实际和可计算的估计可用，事情就会发生变化。这可能是 Lipschitz 连续函数和 Hölder 连续函数的情况，或者更普遍地适用于允许连续模数的函数。假设可以获得一阶导数、分数阶导数或连续性模数的估计值。给出了一些例子。