逆像

本书暂定概念：尚未进入正式概念库。下面是本书给出的定义原文。

定义 · 2.1 映射

可能有不止两个 $X$ 中的元素对应于同一个 $y\in Y$。$X$ 中那些在 $f$ 下被映到 $y\in Y$ 的元素所构成的子集，称为 $y$ 的逆像(inverse image)，记作 $f^{-1}(y)=\{x\in X|f(x)=y\}$。集合 $X$ 称为该映射的定义域(domain)，而 $Y$ 称为该映射的值域(range)。该映射的像(image)为 $f(X)=\{y\in Y|y=f(x)\text{ for some }x\in X\}\subset Y$。像 $f(X)$ 也记作 $\mathrm{im}f$。读者应当注意，若不指明定义域与值域，就无法定义一个映射。以 $f(x)=\exp x$ 为例。若定义域与值域都是 $\mathbb{R}$，则 $f(x)=-1$ 没有逆

英文原文

There may be more than two elements in $X$ that correspond to the same $y\in Y$ . A subset of $X$ whose elements are mapped to $y\in Y$ under $f$ is called the inverse image of $y$ , denoted by $f^{-1}(y)=\{x\in X|f(x)=y\}$ . The set $X$ is called the domain of the map while $Y$ is called the range of the map. The image of the map is $f(X)=\{y\in Y|y=f(x)\text{ for some }x\in X\}\subset Y$ . The image $f(X)$ is also denoted by $\mathrm{im}f$ . The reader should note that a map cannot be defined without specifying the domain and the range. Take $f(x)=\exp x$ , for example. If both the domain and the range are $\mathbb{R}$ , $f(x)=-1$ has no inverse

出处：2.1 映射 · node a-480e17a0a9126161c16bdf51 · 源节点 SHA-256 5a704c4a0d3cceb7…