ThmDex – An index of mathematical definitions, results, and conjectures.

Probability that a continuous random real number takes value in the rational numbers is zero

Formulation 0

Let $X \in \text{Random}(\mathbb{R})$ be a D6096: Continuous random real number.

Then \begin{equation} \mathbb{P}(X \in \mathbb{Q}) = 0 \end{equation}

Proofs

Proof 0

Let $X \in \text{Random}(\mathbb{R})$ be a D6096: Continuous random real number.