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

Result R2615 on D1880: Cofinite set

Empty set is cofinite within a finite set

Formulation 0

Let $X$ be a D17: Finite set.
Let $\emptyset$ be the D13: Empty set.

Then $\emptyset$ is a D1880: Cofinite set within $X$.

Proofs

Proof 0

Let $X$ be a D17: Finite set.
Let $\emptyset$ be the D13: Empty set.

Result R7: Empty set is subset of every set shows that $\emptyset \subseteq X$. Then $X \setminus \emptyset = X$ is finite since we assumed $X$ to be finite. $\square$