Difference between revisions of "Constant"

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===Constant function===
 
===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.
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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===
 
===Constant term of a polynomial===

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

Note that in general, the constant term of a polynomial $f(x_1, \ldots, x_n)$ is simply the value $f(0, \ldots, 0)$.

Examples

$\displaystyle\pi$, or pi is a famous constant that is approximately 3.14159.

$\displaystyle e$, 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.

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