Difference between revisions of "Constant"

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.

@@ Line 1: / Line 1: @@
 == 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.
+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 ==
@@ Line 9: / Line 19: @@
 <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 forever.
+All numbers are constants because they do not change their value; they always remain the same.

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