考虑到ChatGPT的回答质量不高，这次以维基百科的资料作为学习起点。
极限，从生活体验上讲，往往指某个方面的最大，最小，最高，最低，最多，最少的某个量，是一个无法超越的量，比如
参维基百科·极限中列出的相关条目。有关拓扑学和范畴论的中的极限定义，我现在几乎完全不能理解，这里先不强行记录了（不献丑），具体可以参看前面的链接。
極限分為描述一个序列的下標愈來越大时的趋势（序列極限），或是描述函数的自变量接趨近某個值時的函数值的趋势（函數極限）(参)
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. (Ref)
函數極限描述函數在接近某一給定自變量時的特徵。 函數$f$於$a$的極限為$L$，直觀上意為當$x$無限接近$a$時，$f(x)$便無限接近$L$。(参)
(ε, δ)-definition of limit (Ref) (这是在实数域上函数极限的严格定义)
Suppose ${\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} }$ is a function defined on the real line, and there are two real numbers $p$ and $L$. One would say that the limit of $f$, as $x$ approaches $p$, is $L$ and written
${\displaystyle \lim _{x\to p}f(x)=L}$,
or alternatively, say ${\textstyle {\boldsymbol {f(x)}}}$ tends to ${\textstyle {\boldsymbol {L}}}$ as ${\textstyle {\boldsymbol {x}}}$ tends to ${\textstyle {\boldsymbol {p}}}$, and written:
${\displaystyle f(x)\to L\;\;{\text{as}}\;\;x\to p}$,
if the following property holds: for every real $ε > 0$, there exists a real $δ > 0$ such that for all real $x$, $0 < \vert x − p \vert < δ$ implies $\vert f(x) − L \vert < ε$. Symbolically,
\[{\displaystyle (\forall \varepsilon >0)\,(\exists \delta >0)\,(\forall x\in \mathbb {R} )\,(0<\vert x-p \vert <\delta \implies \vert f(x)-L \vert <\varepsilon )}.\]極限為某些數列才擁有的特殊值，當數列的下標越來越大的時候，數列的值也就越接近那個特殊值。（参）
In mathematics, the limit of a sequence is the value that the terms of a sequence “tend to”, and is often denoted using the
${\displaystyle \lim _{n\to \infty}a_n}$.
(Ref)