# term

term / tərm/ •
n. 1. a word or phrase used to describe a thing or to express a concept, esp. in a particular kind of language or branch of study: *the musical term “leitmotiv”* | *a term of abuse.* ∎ (terms) language used on a particular occasion; a way of expressing oneself: *a protest in the strongest possible terms.* ∎ Logic a word or words that may be the subject or predicate of a proposition.2. a fixed or limited period for which something, e.g., office, imprisonment, or investment, lasts or is intended to last: *the president is elected for a single four-year term.* ∎ archaic the duration of a person's life. ∎ (also full term) the completion of a normal length of pregnancy: *the pregnancy went to full term*

*low birthweight*∎ Law a tenancy of a fixed period. ∎ archaic a boundary or limit, esp. of time.3. each of the periods in the year, alternating with holidays or vacations, during which instruction is given in a school, college, or university, or during which a court holds sessions:

**at term**.*the summer term*

*term starts tomorrow.*4. (terms) conditions under which an action may be undertaken or agreement reached; stipulated or agreed-upon requirements:

*the union and the company agreed upon the contract's terms*|

*he could only be dealt with*∎ conditions with regard to payment for something; stated charges:

**on his own terms**.*loans on favorable terms.*∎ agreed conditions under which a war or other dispute is brought to an end:

*a deal in Bosnia that could force the Serbs to*5. Math. each of the quantities in a ratio, series, or mathematical expression.6. Archit. another term for terminus.• v. [tr.] give a descriptive name to; call by a specified name:

**come to terms**.*he has been termed the father of modern theology.*PHRASES: come to terms with come to accept (a new and painful or difficult event or situation); reconcile oneself to:

*she had come to terms with the tragedies in her life.*in terms of (or in —— terms) with regard to the particular aspect or subject specified:

*replacing the printers is difficult to justify in terms of cost*|

*sales are down by nearly 7 percent in*the long/short/medium term used to refer to a time that is a specified way into the future.on —— terms in a specified relation or on a specified footing:

**real terms**.*we are all on friendly terms.*

# term

**term** An expression formed from symbols for functions, constants, and variables. An example is *f*(*a,g*(*h*(*b*)*,c,d*))

Terms are defined recursively as follows: a term is either a variable symbol, a constant symbol, or else has the form φ(τ_{1},…,τ* _{k}*), where φ is a function symbol and each of τ

_{1},…,

*τ*is itself a term. The example above thus has the overall form

_{k}*f*(τ

_{1},τ

_{2}): in this case φ =

*f*and

*k*= 2. Another constraint is that different occurrences of the same symbol φ cannot occur with different values of

*k*, i.e. each φ must have a fixed

*arity*(number of arguments). Thus

*f*(

*a,f*(

*h*(

*b*)

*,c,d*))

would not be a term since the first

*f*has arity 2 while the second has arity 3; neither would

*f*(

*a,g*(

*h*(

*b*)

*,c,h*)),

since the first

*h*has arity 1 while the second has arity 0.

Terms are often built using signatures. A Σ-

*term*is a term in which each constant and function symbol used is in a signature Σ, and has the arity associated with it by Σ and, if Σ is a many-sorted signature, all the sorts match properly. A Σ-term is also called a

*term over signature*Σ. Often a Σ-term is allowed to contain variables (of arity 0) in addition to symbols in Σ. Terms containing variables are called

*open terms*; terms containing only symbols of the signature are called

*closed*or

*ground terms*. Terms can also be viewed as trees (see tree language). Terms (whether as expressions or as trees) are important in the construction of virtually all syntactic concepts. Terms as defined here are sometimes called

*first-order terms*, to distinguish them from the

*higher-order terms*(such as those involved in lambda calculus). See also predicate calculus, initial algebra, equation.

# Term

# Term

A term is an algebraic expression which can form a separable part of another expression such as an algebraic equation or a sequence. Terms are a specific part of the symbolic language of algebra. The symbols of this language were primarily developed during the sixteenth and seventeenth centuries and are used to represent otherwise lengthy expressions. They can be as simple as using the single character, +, to mean addition, or as complicated as y = 4x^{2} + 2x - 3 to represent an algebraic polynomial equation.

In general, there are three types of algebraic expressions which can be classified as terms. These include expressions made up of a single variable or constant, ones that are the product or quotient of two or more variables and/or constants, and those that are the product or quotient of other expressions. For example, the number 4 and the variable x are both terms because they consist of a single symbol. The expression 2z is also a term because it represents the product of two symbols. It should be noted that terms like 2z, in which a number and a variable are written together, are indicated products because multiplication is implied. Therefore, the symbol 2z means 2 × z. Finally, an expression like 2pq (a + 5)n is a term because it represents a quotient (the result of division) of two expressions.

The symbols that make up a term are known as coefficients. In the term 4x, the number 4 is known as a numerical coefficient and the letter x is known as the literal coefficient. For this expression, we could say that 4 is the coefficient of x or x is the coefficient of 4.

Terms should be thought of as a single unit that represents the value of a particular number. This is particularly useful when discussing the terms of a larger expression such as an equation. In the expression 5x^{3} + 2x^{2} + 4x - 7, there are four terms. Numbering them from left to right, the first term is 5x^{3}, the second is 2x^{2}, the third is 4x, and the fourth is -7. Notice that the sign in front of a term is actually part of it.

Some expressions contain terms which can be combined to form a single term. These “like terms” contain the same variable raised to the same power. For example, the like terms in the expression 3x + 2x can be added and the equation simplifies to 5x. Similarly, the expression 7y^{2} - 3y^{2} can be simplified to 4y^{2}. Expressions containing unlike terms can not be simplified. Therefore, 4x^{2} - 2x is in its simplest form because the differences in the power of x prevents these terms from being combined.

# Term

# Term

A term is an algebraic expression which can form a separable part of another expression such as an algebraic equation or a sequence. Terms are a specific part of the symbolic language of **algebra** . The symbols of this language were primarily developed during the sixteenth and seventeenth centuries and are used to represent otherwise lengthy expressions. They can be as simple as using the single character, +, to mean addition, or as complicated as y = 4x2 + 2x - 3 to represent an algebraic polynomial equation.

In general, there are three types of algebraic expressions which can be classified as terms. These include expressions made up of a single **variable** or constant, ones that are the product or quotient of two or more variables and/or constants, and those that are the product or quotient of other expressions. For example, the number 4 and the variable x are both terms because they consist of a single symbol. The expression 2z is also a term because it represents the product of two symbols. It should be noted that terms like 2z, in which a number and a variable are written together, are indicated products because **multiplication** is implied. Therefore, the symbol 2z means 2 × z. Finally, an expression like 2pq(a + 5)n is a term because it represents a quotient (the result of **division** ) of two expressions.

The symbols that make up a term are known as coefficients. In the term 4x, the number 4 is known as a numerical **coefficient** and the letter x is known as the literal coefficient. For this expression, we could say that 4 is the coefficient of x or x is the coefficient of 4.

Terms should be thought of as a single unit that represents the value of a particular number. This is particularly useful when discussing the terms of a larger expression such as an equation. In the expression 5x3 + 2x2 + 4x - 7, there are four terms. Numbering them from left to right, the first term is 5x3, the second is 2x2, the third is 4x, and the fourth is -7. Notice that the sign in front of a term is actually part of it.

Some expressions contain terms which can be combined to form a single term. These "like terms" contain the same variable raised to the same power. For example, the like terms in the expression 3x + 2x can be added and the equation simplifies to 5x. Similarly, the expression 7y2 - 3y2 can be simplified to 4y2. Expressions containing unlike terms can not be simplified. Therefore, 4x2 2x is in its simplest form because the differences in the power of x prevents these terms from being combined.

# Term

# TERM

*An expression, word, or phrase that has a fixed and known meaning in a particular art, science, or profession. A specified period of time.*

The term of a court is the legally prescribed period for which it may be in session. Although the session of the court is the time that it actually sits, the words *term* and *session* are frequently used interchangeably.

In reference to a lease, a term is the period granted during which the lessee is entitled to occupy the rented premises. It does not include the period of time between the creation of the lease and the entry of the tenant. Similarly when used in reference to estates, the term is the period of time for which an estate is granted. An estate for five years, for example, is one with a five-year term.

A term of office is the time during which an official who has been appointed or elected may hold the office, perform its functions, and partake of its emoluments and privileges.

# term

**term** limit in time, period XIII; (pl.) limiting conditions XIV; form in which a matter or subject is expressed, expression. — (O)F. *terme* :- L. *terminus* limit, boundary.

So **terminal** pert. to a boundary XV; situated at or forming the end XIX; sb. terminal element XIX. — L.; see -AL1. **terminate** †determine XVI; bring to an end XVI. f. pp. stem of L. *termināre*; see -ATE3. **termination** †determination; end XV; (gram.) ending XVI. — (O)F. or L. **terminology** system of terms. XIX. — G. *terminologie*. **terminus** pl. *-i* finishing point XVII; end of a line of railway XIX. — L.

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