Denote

Denote is a verb meaning to be a sign of, to indicate, or to designate something by a name, symbol, or label. It can also mean to refer to or to identify a particular object, value, or concept. The noun form denotation refers to the explicit reference or literal meaning of a word, phrase, or symbol, as opposed to its connotations or emotional associations.

In mathematics, logic, and formal disciplines, denote is used to assign a symbol or expression to a specific object or set. For example, Let N denote the set of natural numbers. The symbol ∑ denotes the sum of a sequence. In linguistics and philosophy, the denotation of a term is the set of all entities it applies to; the denotation of "cat" is the collection of all cats.

Denote is often contrasted with signify and indicate. Denote tends to emphasize literal reference or designation, while signify can be broader, capturing symbolic meaning or cultural significance, and indicate emphasizes pointing out a fact or feature. In practical writing, denote is commonly used when defining terms, referencing symbols, or specifying how a term should be interpreted within a formal system.

Etymology traces denote to Latin denotare, from de- plus notare, meaning to mark out or to note. The term appears across disciplines wherever a precise reference or symbol-based designation is required.