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Inverse Map

  • Inverse Map #Card
    • Denoted by $f^{-1} : Y \to X$, exists only if $f$ is bijective, and satisfies $x = f^{-1}(y) \iff f(x) = y$. - Note: We distinguish between the inverse relation $f^-$ (exists for any map, $f^-(y) \subset X$) and the inverse map $f^{-1}$ (exists only for bijections, ${f^{-1}(y)} = f^-(y)$).

Back

Section titled “Back”

Denoted by $f^{-1} : Y \to X$, exists only if $f$ is bijective, and satisfies $x = f^{-1}(y) \iff f(x) = y$.

  • Note: We distinguish between the inverse relation $f^-$ (exists for any map, $f^-(y) \subset X$) and the inverse map $f^{-1}$ (exists only for bijections, ${f^{-1}(y)} = f^-(y)$).

Lean

Section titled “Lean”

Equiv.symm / 部分的には Function.invFun