Cofinite set – TheoremDex

▾ 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

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