Definition:Term of Expression
Definition
A term is either a variable or a constant.
Let $a \circ b$ be an expression.
Then each of $a$ and $b$ are known as the terms of the expression.
The word term is usually used when the operation $\circ$ is addition, that is $+$.
Instances
Term of Fraction
The terms of a fraction are referred to as the numerator and the denominator:
Numerator
The term $a$ is known as the numerator of $\dfrac a b$.
Denominator
The term $b$ is known as the denominator of $\dfrac a b$.
A helpful mnemonic to remember which goes on top and which goes on the bottom is "Numerator Over Denominator", which deserves a "nod" for being correct.
Term of Polynomial
Let $P = a_n x^n + a_{n - 1} x^{n - 1} + \cdots + a_1 x + a_0$ be a polynomial.
Each of the expressions $a_i x^i$, for $0 \le i \le n$, is referred to as a term of $P$.
Term of Sequence
The elements of a sequence are known as its terms.
Let $\sequence {x_n}$ be a sequence.
Then the $k$th term of $\sequence {x_n}$ is the ordered pair $\tuple {k, x_k}$.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): term: 1.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): term: 1.
- 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $1$: Elementary, my dear Watson: $\S 1.1.1$: 'You talking to me?': Definition $1.1.4$
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): term: 1.