ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5643 on D2183: Set of bytes
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
Proof 0
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} $\square$