Let $|\cdot|$ be the D2184: Set cardinality operation.

Then
\begin{equation}
\left| \{ 0, 1 \}^8 \right|
= 256
\end{equation}

Result R5643
on D2183: Set of bytes

*Subresult of R1832: Cardinality of a finite cartesian product of finite sets*

Cardinality of the set of bytes

Formulation 0

Let $|\cdot|$ be the D2184: Set cardinality operation.

Then
\begin{equation}
\left| \{ 0, 1 \}^8 \right|
= 256
\end{equation}

Proofs

Let $|\cdot|$ be the D2184: Set cardinality operation.

Applying the result R1832: Cardinality of a finite cartesian product of finite sets, we have
\begin{equation}
\left| \{ 0, 1 \}^8 \right|
= | \{ 0, 1 \} |^8
= 2^8
= 256
\end{equation}
$\square$