Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that

(i)	$F : \mathbb{R} \to [0, 1]$ is a D205: Probability distribution function for $X$

The quantile function of $X$ is the D4364: Real function \begin{equation} [0, 1] \to \mathbb{R}, \quad x \mapsto \inf \left\{ t \in \mathbb{R} : x \leq F(t) \right\} \end{equation}

Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number.
The quantile function of $X$ is the D4364: Real function \begin{equation} [0, 1] \to \mathbb{R}, \quad x \mapsto \inf \left\{ t \in \mathbb{R} : x \leq \mathbb{P}(X \leq t) \right\} \end{equation}