In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, and particularly in formal algebra

Algebra

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...

, an indeterminate is a symbol that does not stand for anything else but itself. In particular it does not designate a constant, or a parameter

Parameter

Parameter from Ancient Greek παρά also “para” meaning “beside, subsidiary” and μέτρον also “metron” meaning “measure”, can be interpreted in mathematics, logic, linguistics, environmental science and other disciplines....

 of the problem, it is not an unknown that could be solved for, it is not a variable

Variable (mathematics)

In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...

 designating a function argument, or being summed or integrated over, or any other type of bound variable. Indeterminates are used to build formal objects such as polynomial

Polynomial

In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...

s, formal power series

Formal power series

In mathematics, formal power series are a generalization of polynomials as formal objects, where the number of terms is allowed to be infinite; this implies giving up the possibility to substitute arbitrary values for indeterminates...

, or elements of a free group

Free group

In mathematics, a group G is called free if there is a subset S of G such that any element of G can be written in one and only one way as a product of finitely many elements of S and their inverses...

.

Example

The distinction between an unknown and an indeterminate can be illustrated as follows.

1. Let be an unknown satisfying,
where a and b are given number

Number

A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....

s (or parameters). Then, provided b is not 3, we can solve for x, to find,
while for b = 3 the problem either has no solution at all, or, if also a = 2, it admits any value for x as solution.

2. Let be an indeterminate, and a, b as above. Then,
does not hold unless a = 2 and b = 3. This is because X is not, and does not designate, a number; the only way can hold is when both sides of the equation are 0.