Definition:Summation/Index Variable

This page is about Index Variable of Summation in the context of algebra. For other uses, see index.

Definition

Consider the summation, in either of the three forms:

$\ds \sum_{j \mathop = 1}^n a_j \qquad \sum_{1 \mathop \le j \mathop \le n} a_j \qquad \sum_{\map R j} a_j$

The variable $j$, an example of a bound variable, is known as the index variable of the summation.

Also known as

The index variable of a summation can also be seen referred to as dummy variable or dummy index.

Linguistic Note

The plural of index is indices.

Compare vertex and apex, which have a similar plural form.

Sources

• 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $2$: Integers and natural numbers: $\S 2.1$: The integers
• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.3$: Sums and Products