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
Empty set is cofinite within a finite set