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Term (logic) : ウィキペディア英語版
Term (logic)
In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact. In particular, terms appear as components of a formula.
A first-order term is recursively constructed from constant symbols, variables and function symbols.
An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation.
For example, (''x''+1)
*(''x''+1) is a term built from the constant 1, the variable ''x'', and the binary function symbols + and
*; it is part of the atomic formula (''x''+1)
*(''x''+1) ≥ 0 which evaluates to true for each real-numbered value of ''x''.
Besides in logic, terms play important roles in universal algebra, and rewriting systems.
==Elementary mathematics==
In the context of polynomials, sometimes ''term'' is used for a monomial with a coefficient: to 'collect like terms' in a polynomial is the operation of making it a linear combination of distinct monomials. Terms, in this sense, are things that are added or subtracted.
A series is often represented as the sum of a sequence of terms.
Individual factors in an expression representing a product are multiplicative terms.
For example, in 6 + 3''x'' − 2, 6, 3''x'', and −2 are all terms.
In elementary mathematics,
* each argument term of the addition operator + is called an ''addend'',
* the first and second argument term of the subtraction operator - is called a ''minuend'' and ''subtrahend'', respectively,
* each argument term of the multiplication operator ⋅ is called a ''factor'', the first and second argument term is also called ''multiplicand'' and ''multiplier'', respectively,
* the first and second argument term of the division operator / is called ''dividend'' and ''divisor'', respectively,
* if the division operator is written as fraction bar, the top and bottom terms are called ''numerator'' and ''denominator'', respectively.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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