# Mathematical Term

A Mathematical Term is Mathematical Object that is a component of a Mathematical Formula.

## References

### 2020b

1. Becker, T. and Weispfenning, V. Gröbner Bases: "A Computational Approach to Commutative Algebra". New York: Springer-Verlag, 1993.
2. Lichtblau, D. “Grobner Bases in Mathematica 3.0." Mathematica J. 6, 81-88, 1996.

### 2020c

• (Encyclopedia of Mathematics, 2020) ⇒ https://www.encyclopediaofmath.org/index.php/Term Retrieved: 2020-03-26.
• QUOTE: A linguistic expression used to denote objects. For example, the expressions $1,0+1,\lim_{x\to0}(\sin x)/x$ are distinct terms denoting the same object. A term can contain free variables (parameters) (cf. Free variable), fixation of whose values uniquely defines some object according to the semantic laws of the language — the value of the term for the given values of its free variables. Thus, if $f$ is a variable with as values integrable real-valued functions, and $x$, $a$, $b$ are variables whose values are real numbers, then the expression $\int_a^bf(x)dx$ is a term with three parameters $a$, $b$, $f$, which denotes a well-defined real number for each set of values of the parameters ($x$ in this term is a bound variable). Syntactically, terms are characterized by the fact that they can be substituted for variables in other expressions of the language — terms or formulas, yielding new terms or formulas, respectively.

In a formalized language there exist formal rules, independent of the semantics of the language, for constructing terms and distinguishing free variables in them. In many-sorted languages there are also rules for determining the sorts of the terms which occur.

### 2020d

• The sum of a series of related numbers can be expressed through capital sigma notation, which compactly denotes iteration. For example,

$\displaystyle{ \sum_{k=1}^5 k^2 = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 55. }$

1. Department of the Army (1961) Army Technical Manual TM 11-684: Principles and Applications of Mathematics for Communications-Electronics. Section 5.1
2. Shmerko, V.P.; Yanushkevich [Ânuškevič], Svetlana N. [Svitlana N.]; Lyshevski, S.E. (2009). Computer arithmetics for nanoelectronics. CRC Press. p. 80.
3. Hosch, W.L. (Ed.). (2010). The Britannica Guide to Numbers and Measurement. The Rosen Publishing Group. p. 38
4. and
5. Schwartzman p. 19
6. "Addend" is not a Latin word; in Latin it must be further conjugated, as in numerus addendus "the number to be added".

### 2020e

• (Simple Wikipedia, 2020) ⇒ https://simple.wikipedia.org/wiki/Term_(mathematics) Retrieved:2020-3-26.
• In elementary mathematics, a term is either a single number or variable, or the product of several numbers or variables. Terms are separated by a + or - sign in an overall expression. For example, in

$3 + 4x + 5yzw$

$3$, $4x$, and $5yzw$ are three separate terms.

In the context of polynomials, term can mean a monomial with a coefficient. To 'combine like terms' in a polynomial is the basic operation of making it a linear combination of distinct monomials. For example,

$3 x + 2x^2 + 5x + 1 = 2x^2 + (3+5)x + 1 = 2x^2 + 8x + 1$, with like terms collected.

A series is often represented as the sum of a sequence of terms.

In general mathematical use, however, term is not limited to additive expressions. Individual factors in an expression representing a product are multiplicative terms. Indeed, individual elements of any mathematical expression may be referred to as "terms".

﻿ ﻿Terms also appear in logic.