Difference between revisions of "Constant"

m (when discussing polynomials)
m
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
== 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 a number that remains the same, unlike a [[variable]], that can change. When discussing polynomials, the '''constant''' or constant term is the coefficient of <math>x^0</math>.
+
 
 +
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 ==

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.

Invalid username
Login to AoPS