mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable...

Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union...

mathematics, an axiom of countability is a property of certain mathematical objects that asserts the existence of a countable set with certain properties...

null set is a Lebesgue measurable set of real numbers that has measure zero. This can be characterized as a set that can be covered by a countable union...

In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. The set of natural numbers (whose existence...

In mathematics, an Fσ set (said F-sigma set) is a countable union of closed sets. The notation originated in French with F for fermé (French: closed) and...

formulate probability theory on sets which are constrained to be measurable. The measurable sets on the line are iterated countable unions and intersections...

In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets. The inductive definition above is well-founded...

V=L Axiom of countability Every set is hereditarily countable Axiom of countable choice The product of a countable number of non-empty sets is non-empty...

finite set is finite. All finite sets are countable, but not all countable sets are finite. (Some authors, however, use "countable" to mean "countably infinite"...