# Definition:Constant

## Definition

A **constant** is a name for an object (usually a number, but the concept has wider applications) which *does not change* during the context of a logical or mathematical argument.

A constant can be considered as an operator which takes no operands.

A constant can also be considered as a variable whose domain is a singleton.

## Also known as

A **constant** in an expression in algebra is also seen referred to as an **absolute term**.

In the same context, the term **literal (constant)** can sometimes be seen in order to differentiate it from a numerical constant

## Also see

- Definition:Proper Name (as used, usually, in the context of predicate logic)
- Definition:Constant Mapping
- Definition:Constant (Category Theory)
- Definition:Constant Polynomial
- Definition:Arbitrary Constant

## Historical Note

The term **constant**, as opposed to a variable, was introduced by Gottfried Wilhelm von Leibniz.

## Linguistic Note

The word **constant** can be used either as a noun:

*Let $c$ be a constant between $0$ and $1$*

or as an adjective:

*Let $c$ be a constant real number between $0$ and $1$*

Which is intended can usually be deduced from the context.

## Sources

- 1910: Alfred North Whitehead and Bertrand Russell:
*Principia Mathematica: Volume $\text { 1 }$*... (previous) ... (next): Chapter $\text{I}$: Preliminary Explanations of Ideas and Notations - 1914: G.W. Caunt:
*Introduction to Infinitesimal Calculus*... (next): Chapter $\text I$: Functions and their Graphs: $1$. Constants and Variables - 1919: Horace Lamb:
*An Elementary Course of Infinitesimal Calculus*(3rd ed.) ... (previous) ... (next): Chapter $\text I$. Continuity: $1$. Continuous Variation - 1946: Alfred Tarski:
*Introduction to Logic and to the Methodology of Deductive Sciences*(2nd ed.) ... (previous) ... (next): $\S 1.1$: Constants and variables - 1972: Murray R. Spiegel and R.W. Boxer:
*Theory and Problems of Statistics*(SI ed.) ... (previous) ... (next): Chapter $1$: Discrete and Continuous Variables - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**literal**:**1.** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**absolute term** - 2008: David Joyner:
*Adventures in Group Theory*(2nd ed.) ... (previous) ... (next): Chapter $1$: Elementary, my dear Watson: $\S 1.1.1$: 'You talking to me?': Definition $1.1.4$ - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**absolute term**