ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4314 on D15: Set cardinality
Number of boolean functions on a finite set
Formulation 0
Let $X$ be a D17: Finite set such that
(i) $\mathcal{M} : = \{ 0, 1 \}^X$ is the D68: Set of maps from $X$ to $\{ 0, 1 \}$
Then \begin{equation} |\mathcal{M}| = 2^{|X|} \end{equation}
Proofs
Proof 0
Let $X$ be a D17: Finite set such that
(i) $\mathcal{M} : = \{ 0, 1 \}^X$ is the D68: Set of maps from $X$ to $\{ 0, 1 \}$
This result is a particular case of R1856: Cardinality of the set of maps between finite sets. $\square$