Let $\mathbb{N}$ be the D225: Set of natural numbers.
The standard Hilbert cube is the D11: Set \begin{equation} \prod_{n \in \mathbb{N} + 1} [0, 1 / n] \end{equation}

Let $\mathbb{N}$ be the D225: Set of natural numbers.
The standard Hilbert cube is the D11: Set \begin{equation} \prod_{n = 1}^{\infty} \textstyle [0, \frac{1}{n}] \end{equation}

Let $\mathbb{N}$ be the D225: Set of natural numbers.
The standard Hilbert cube is the D11: Set \begin{equation} \textstyle [0, 1] \times [0, \frac{1}{2}] \times [0, \frac{1}{3}] \times [0, \frac{1}{4}] \times \cdots \end{equation}