Definition:Summation/Index Variable
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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