ThmDex – An index of mathematical definitions, results, and conjectures.

Result R4314 on D15: Set cardinality
Subresult of R1856: Cardinality of the set of maps between finite sets

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}

Subresults

▶	R5094: Number of boolean functions on a boolean cartesian product

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. $\square$