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
  • Definition:Constant of Integration

• Definition:Constant (Physics)
• Definition:Physical Constant

• Definition:Absolute Number

• Definition:Variable

• Results about constants can be found here.

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): literal: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): absolute term
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): constant: 1.
• 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): absolute term
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): constant: 1.