# Constant

*in mathematical logic*

A symbol of a formal language for denoting some fixed element (individual), a fixed operation or relation on some structure described by this language. In this connection one distinguishes between individual constants (cf. Individual constant), function constants and predicate constants. The set of constants of a language is called the *signature* of this language. For example, in one presentation, the signature of the language of formal arithmetic (cf. Arithmetic, formal) may consist of the individual constant "$0$" (zero), the two-place function constants "$+$" (addition) and "$\cdot$" (multiplication), the one-place function constant "'$'$" (successor) and the two-place predicate constant "$=$" (equality).

#### Comments

The term "constant" is also used for non-varying elements in all kinds of expressions, e.g. the constants of a polynomial (also called its coefficients, cf. Coefficient), field constants (when considering some construct over a field, the elements of the field itself are often called constants), etc.

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Constant.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Constant&oldid=37036