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For example, 2+2 is a ground term and hence also a linear term, x⋅(n+1) is a linear term, n⋅(n+1) is a non-linear term. These properties are important in, for example, term rewriting. Given a signature for the function symbols, the set of all terms forms the free term algebra. The set of all ground terms forms the initial term algebra.
This section features terms used across different areas in mathematics, or terms that do not typically appear in more specialized glossaries. For the terms used only in some specific areas of mathematics, see glossaries in Category:Glossaries of mathematics .
In mathematics, a constant term (sometimes referred to as a free term) is a term in an algebraic expression that does not contain any variables and therefore is constant. For example, in the quadratic polynomial, + +, The number 3 is a constant term. [1]
In this example a, b and c are coefficients of the polynomial. Since c occurs in a term that does not involve x, it is called the constant term of the polynomial and can be thought of as the coefficient of x 0. More generally, any polynomial term or expression of degree zero (no variable) is a constant. [5]: 18
Term (logic), a component of a logical or mathematical expression (not to be confused with term logic, or Aristotelian logic) Ground term, a term with no variables; Addend, or term, an operand to the addition operator Term of a summation, a polynomial, or a series, a special case of a summand; Term algebra, a freely generated algebraic structure
As one example, () = is undefined when =. As division by zero is undefined in algebra, = is not part of the domain of (). Contrast the term primitive notion, which is a core concept not defined in terms of other concepts. Primitive notions are used as building blocks to define other concepts.
The examples 1 and 2 denote different terms, differing only in where the parentheses are placed. They have different meanings: example 1 is a function definition, while example 2 is a function application. The lambda variable x is a placeholder in both examples. Here, example 1 defines a function .
Aristotle also thought that quantity alone does not distinguish mathematics from sciences like physics; in his view, abstraction and studying quantity as a property "separable in thought" from real instances set mathematics apart. [5] Auguste Comte's definition tried to explain the role of mathematics in coordinating phenomena in all other ...