# Definition:Ordered Tuple/Notation

## Definition

Notation for an ordered tuple varies throughout the literature.

There are also specialised instances of an ordered tuple where the convention is to use angle brackets.

However, it is common for an ordered tuple to be denoted:

- $\tuple {a_1, a_2, \ldots, a_n}$

extending the notation for an ordered pair.

For example: $\tuple {6, 3, 3}$ is the ordered triple $f$ defined as:

- $\map f 1 = 6, \map f 2 = 3, \map f 3 = 3$

The notation:

- $\sequence {a_1, a_2, \ldots, a_n}$

is recommended when use of round brackets would be ambiguous.

Other notations which may be encountered are:

- $\sqbrk {a_1, a_2, \ldots, a_n}$
- $\set {a_1, a_2, \ldots, a_n}$

but both of these are strongly discouraged: the square bracket format because there are rendering problems on this site, the latter because it is too easily confused with set notation.

In order to further streamline notation, it is common to use the more compact $\sequence {a_n}$ for $\sequence {a_k}_{1 \mathop \le k \mathop \le n}$.

Some sources, particularly in such fields as communication theory, where the elements of the domain of the ordered tuple is a specific set of symbols, use the notation $x_1 x_2 \cdots x_n$ for $\tuple {x_1, x_2, \dotsc, x_n}$.

## Sources

- 1988: Dominic Welsh:
*Codes and Cryptography*... (previous) ... (next): Notation