# Definition:Term (Algebra)

## 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 "**N**umerator **O**ver **D**enominator", 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): Entry:**term**:**1.** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**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): Entry:**term**:**1.**