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

Result R4189 on D15: Set cardinality
Subresult of R1846: Cardinality of set complement

Formulation 0

Let $X$ be a D17: Finite set such that

(i)	$E \subseteq X$ is a D78: Subset of $X$

Then \begin{equation} |X \setminus E| = |X| - |E| \end{equation}

Subresults

▶	R4188: Set cardinality in terms of finite ambient set

Proofs

Proof 0

Let $X$ be a D17: Finite set such that

(i)	$E \subseteq X$ is a D78: Subset of $X$

Since $X$ is finite, result R477: Set finiteness is hereditary guarantees that also $E$ is finite. Hence, this result is a particular case of R1846: Cardinality of set complement. $\square$