Term (logic)
In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact. In particular, terms appear as components of a formula.
A first-order term is recursively constructed from constant symbols, variables and function symbols.
An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation.
For example, is a term built from the constant 1, the variable x, and the binary function symbols and ; it is part of the atomic formula which evaluates to true for each real-numbered value of x.
Besides in logic, terms play important roles in universal algebra, and rewriting systems.
Elementary mathematics
In the context of polynomials, sometimes term is used for a monomial with a coefficient: to 'collect like terms' in a polynomial is the operation of making it a linear combination of distinct monomials. Terms, in this sense, are things that are added or subtracted.
A series is often represented as the sum of a sequence of terms.
Individual factors in an expression representing a product are multiplicative terms.
For example, in 6 + 3x − 2, 6, 3x, and −2 are all terms.