A D18: Map $g : Y \to X$ is an inverse of $f$ if and only if
| (1) | \begin{equation} \forall \, x \in X : g(f(x)) = x \end{equation} | (D525: Left inverse map) |
| (2) | \begin{equation} \forall \, y \in Y : f(g(y)) = x \end{equation} | (D526: Right inverse map) |
| ▼ | Set of symbols |
| ▼ | Alphabet |
| ▼ | Deduction system |
| ▼ | Theory |
| ▼ | Zermelo-Fraenkel set theory |
| ▼ | Set |
| ▼ | Binary cartesian set product |
| ▼ | Binary relation |
| ▼ | Inverse binary relation |
| (1) | \begin{equation} \forall \, x \in X : g(f(x)) = x \end{equation} | (D525: Left inverse map) |
| (2) | \begin{equation} \forall \, y \in Y : f(g(y)) = x \end{equation} | (D526: Right inverse map) |
| ▶ | D976: Invertible map |
| ▶ | D702: Involution |
| ▶ | R4543: Map inverse is invertible |
| ▶ | R4542: Map is inverse to its inverse |