Linked from

The 23 pages that link to Countable set, each with the reason it gives.

• Power setRelated: The power set of a countably infinite set is uncountable.

• Georg CantorRelated: Cantor showed that some infinite sets can be listed, while others cannot.

• Continuum hypothesisBroader topic: The natural numbers provide the lower cardinality that the hypothesis bounds.

• CardinalityBroader topic: Countability is the basic test case for comparing infinite cardinalities.

• Probability mass functionRelated: A discrete random variable's possible values form a countable set.

• Transcendental numberRelated: There are countably many algebraic numbers but uncountably many real numbers.

• Cantor's theoremRelated: The theorem implies that the power set of a countable set is uncountable.

• Cantor setCompared with: The Cantor set is uncountable, although each construction stage removes only countably many points in total.

• Baire category theoremRelated: The theorem restricts the union to countably many nowhere-dense sets.

• DiagonalizationNarrower topic: Diagonal arguments test whether a proposed sequence really exhausts a set.

• Cantor's diagonal argumentNarrower topic: The argument challenges whether the real numbers can be listed in this way.

• Cardinal numberBroader topic: Countability identifies the smallest infinite cardinality, shared by the integers and rationals.

• Infinite setCompared with: Countable infinite sets remain listable despite having no finite size.

• InfinityBroader topic: Countability identifies the smallest infinite size shared by the integers and rational numbers.

• Löwenheim–Skolem theoremRelated: A countable language guarantees the theorem's countable-model conclusion.

• Uncountable setCompared with: It is the contrasting size class that an uncountable set exceeds.

• Aleph numberBroader topic: Countably infinite sets have the first infinite aleph, ℵ₀.

• Schröder–Bernstein theoremRelated: Mutual injections can establish countability without constructing an enumeration directly.

• CodeNarrower topic: Countability makes numerical representation possible.

• Hausdorff paradoxRelated: The construction excludes a countable exceptional set where stabilizers obstruct the free action.

• Cardinality of the continuumCompared with: The continuum exceeds countable cardinality, despite the rationals being dense in the reals.

• Lindelöf's lemmaNarrower topic: The base elements and selected cover members are indexed by countable sets.

• Rasiowa–Sikorski lemmaRelated: Countability lets the construction list the dense sets and handle them one at a time.