Indeterminate (variable)

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In mathematics, an indeterminate is a variable that is used formally, without reference to any value. In other words, this is just a symbol used in a formal way.^{[1][2][better source needed]} Indeterminates occur in polynomials, formal power series, and, more generally, in expressions that are viewed as independent mathematical objects.

A fundamental property of an indeterminate is that it can be substituted with any mathematical expressions to which the same operations apply as the operations aplied to the indeterminate.

The concept of an indeterminate is relatively recent, and was initially introduced for distinguishing a polynomial from its associated polynomial function.^{[citation needed]} Indeterminates resemble free variables. The main difference is that a free variable is intended to represent a unspecified element of some domain, often the real numbers, while indeterminates do not represent anything.^{[citation needed]} Many authors do not distinguish indeterminates from other sorts of variables.

Some authors of abstract algebra textbooks define an indeterminate over a ring R as an element of a larger ring that is transcendental over R.^[3][4][5] This uncommon definition implies that every transcendental number and every nonconstant polynomial must be considered as indeterminates.