What does enumerability mean?
Enumerability is the property of being able to count or list a collection as a sequence of distinct members. In everyday discussion it is a formal way of saying that something can be counted, although it is much more common in mathematics, logic, and theoretical computer science. In set theory, a set is enumerable when its elements can be arranged in a sequence without repetition; for an infinite set, this amounts to pairing its members with the natural numbers. The idea is important because it separates the possibility of forming a complete listing from the practical ease of producing one. A set can be infinite yet enumerable, and a procedure may eventually produce every member without giving an immediate way to decide which numbers occur. This is why enumerability appears in classifications of computable problems and countable structures. In ordinary prose, however, countability is usually the clearer and more familiar term, while enumeration usually refers to the act or result of listing items.
nounEnumerability is the quality or property of being enumerable: capable of being counted or listed as a sequence of items. In set theory, it is the property of admitting an enumeration, usually a listing without repetition of all its members.
- The property of being enumerable, especially the capacity of a set or collection to be listed in a sequence without repetition.
"The theorem establishes the enumerability of the set without explicitly displaying the full sequence."
"Mathematicians can often prove the enumerability of a set without displaying the corresponding infinite list."
"In archival research, the enumerability of surviving documents should not be mistaken for the completeness of the surviving record."
Enumerability is normally treated as an uncountable abstract noun, although enumerabilities can occasionally be used for distinct instances in specialized writing.
"The argument concerns the enumerability of the set rather than its numerical size."
An infinite set can still be enumerable—if its members can be placed in a sequence without leaving anything out.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does enumerability come from?
Enumerability was formed in English by combining enumerate with the suffix -ability. Enumerate comes from Latin enumerare, meaning “to count out” or “enumerate,” which was built on numerus, meaning “number.” Related English words include enumerable, enumeration, numeration, and numeral, all reflecting the same Latin root.
How enumerability is actually used
Enumerability is formal and relatively uncommon outside mathematics, logic, and theoretical computer science. In general mathematical English, countability is often the more familiar term, while enumeration usually denotes the act or result of listing.
Easily confused with enumerability
Enumerability is the property of being able to form a complete listing, whereas enumeration is the listing itself or the act of producing it.