Let $X_1, X_2, X_3, \ldots \in \text{Rademacher}(1 / 2)$ each be a D5287: Standard rademacher random integer such that

(i)	$X_1, X_2, X_3, \ldots$ is an D2713: Independent random collection

A D3161: Random real number $Z \in \text{Random}(\mathbb{R})$ is a standard gaussian random real number if and only if \begin{equation} Z \overset{d}{=} \lim_{N \to \infty} \sum_{n = 1}^N \frac{X_n}{\sqrt{N}} \end{equation}