To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time. 4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Languages
Recent
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds # Indeterminate (variable)

In mathematics, and/or particularly in formal algebra, an indeterminate is a symbol that is treated as a variable, does not stand for anything else except itself, and is often used as a placeholder in objects such as polynomials and formal power series. In particular:

## Polynomials

A polynomial in an indeterminate $X$ is an expression of the form $a_{0}+a_{1}X+a_{2}X^{2}+\ldots +a_{n}X^{n}$ , where the $a_{i}$ are called the coefficients of the polynomial. Two such polynomials are equal only if the corresponding coefficients are equal. In contrast, two polynomial functions in a variable $x$ may be equal or not at a particular value of $x$ .

For example, the functions

$f(x)=2+3x,\quad g(x)=5+2x$ are equal when $x=3$ and not equal otherwise. But the two polynomials

$2+3X,\quad 5+2X$ are unequal, since 2 does not equal 5, and 3 does not equal 2. In fact,

$2+3X=a+bX$ does not hold unless $a=2$ and $b=3$ . This is because $X$ is not, and does not designate, a number.

The distinction is subtle, since a polynomial in $X$ can be changed to a function in $x$ by substitution. But the distinction is important because information may be lost when this substitution is made. For example, when working in modulo 2, we have that:

$0-0^{2}=0,\quad 1-1^{2}=0,$ so the polynomial function $x-x^{2}$ is identically equal to 0 for $x$ having any value in the modulo-2 system. However, the polynomial $X-X^{2}$ is not the zero polynomial, since the coefficients, 0, 1 and −1, respectively, are not all zero.

## Formal power series

A formal power series in an indeterminate $X$ is an expression of the form $a_{0}+a_{1}X+a_{2}X^{2}+\ldots$ , where no value is assigned to the symbol $X$ . This is similar to the definition of a polynomial, except that an infinite number of the coefficients may be nonzero. Unlike the power series encountered in calculus, questions of convergence are irrelevant (since there is no function at play). So power series that would diverge for values of $x$ , such as $1+x+2x^{2}+6x^{3}+\ldots +n!x^{n}+\ldots \,$ , are allowed.

## As generators

Indeterminates are useful in abstract algebra for generating mathematical structures. For example, given a field $K$ , the set of polynomials with coefficients in $K$ is the polynomial ring with polynomial addition and multiplication as operations. In particular, if two indeterminates $X$ and $Y$ are used, then the polynomial ring $K[X,Y]$ also uses these operations, and convention holds that $XY=YX$ .

Indeterminates may also be used to generate a free algebra over a commutative ring $A$ . For instance, with two indeterminates $X$ and $Y$ , the free algebra $A\langle X,Y\rangle$ includes sums of strings in $X$ and $Y$ , with coefficients in $A$ , and with the understanding that $XY$ and $YX$ are not necessarily identical (since free algebra is by definition non-commutative).