Let $[0, 1]$ be the D1510: Closed real unit interval such that

(i)	$\mathcal{P} [0, 1]$ is the D80: Power set of $[0, 1]$

A D3639: Standard sequence $C : \mathbb{N} \to \mathcal{P}[0, 1]$ is a standard cantor sequence if and only if

(1)	\begin{equation} C_0 = [0, 1] \end{equation}
(2)	\begin{equation} \forall \, n \in 1, 2, 3, \ldots : C_n = \frac{1}{3} C_{n - 1} \cup \left( \frac{1}{3} C_{n - 1} + \frac{2}{3} \right) \end{equation}