ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Bijective map
▼ Set of bijections
▼ Countable set
▼ Finite set
Definition D1880
Cofinite set
Formulation 0
Let $X$ be a D11: Set.
A D11: Set $E \subseteq X$ is cofinite within $X$ if and only if $X \setminus E$ is a D17: Finite set.
Formulation 1
Let $X$ be a D11: Set.
A D11: Set $E \subseteq X$ is cofinite within $X$ if and only if \begin{equation} |X \setminus E| < \infty \end{equation}
Results
▶ R2615: Empty set is cofinite within a finite set