# Difference between revisions of "Constant"

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== Definition == | == Definition == | ||

+ | A '''constant''' is a number with fixed value, unlike a [[variable]] that can change or that is used to represent an unknown value. | ||

− | A '''constant''' is | + | |

+ | The word constant is also used in other contexts or as part of other expressions: | ||

+ | |||

+ | ===Constant function=== | ||

+ | A [[constant function]] is a [[function]] which has a constant output: the value of the function does not depend on the value of its input. Equivalently, a constant function is a function whose [[range]] has only a single value. | ||

+ | |||

+ | ===Constant term of a polynomial=== | ||

+ | The '''constant term''' of a [[polynomial]] in variables <math>x_1, x_2, \ldots, x_n</math> is the [[coefficient]] of <math>x_1^0\cdot x_2^0 \cdots x_n^0</math>. In the case of a polynomial in a single variable <math>x</math>, it is the coefficient of the term <math>x_0^0</math>. Normally, when we write out a polynomial, the constant term is the term with no variables present, e.g. for the polynomial <math>f(x) = x^3 + 2x^2 - 3x - 7</math>, the constant term is <math>-7</math>. | ||

+ | |||

+ | Note that in general, the constant term of a polynomial <math>f(x_1, \ldots, x_n)</math> is simply the value <math>f(0, \ldots, 0)</math>. | ||

== Examples == | == Examples == | ||

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<math>\displaystyle e</math>, or [[e]] is another famous constant that is approximately 2.71828. | <math>\displaystyle e</math>, or [[e]] is another famous constant that is approximately 2.71828. | ||

− | All numbers are constants because they do not change their value; they remain the same | + | All numbers are constants because they do not change their value; they always remain the same. |

## Latest revision as of 18:39, 30 January 2007

## Definition

A **constant** is a number with fixed value, unlike a variable that can change or that is used to represent an unknown value.

The word constant is also used in other contexts or as part of other expressions:

### Constant function

A constant function is a function which has a constant output: the value of the function does not depend on the value of its input. Equivalently, a constant function is a function whose range has only a single value.

### Constant term of a polynomial

The **constant term** of a polynomial in variables is the coefficient of . In the case of a polynomial in a single variable , it is the coefficient of the term . Normally, when we write out a polynomial, the constant term is the term with no variables present, e.g. for the polynomial , the constant term is .

Note that in general, the constant term of a polynomial is simply the value .

## Examples

, or pi is a famous constant that is approximately 3.14159.

, or e is another famous constant that is approximately 2.71828.

All numbers are constants because they do not change their value; they always remain the same.