Definition:Concatenation of Ordered Tuples

This page is about Concatenation in the context of Ordered Tuple. For other uses, see Concatenation.

Definition

Let $S$ be a set.

Let $w, w'$ be ordered tuples in $S$ of lengths $n$ and $n'$, respectively.

Then the concatenation of $w$ and $w'$, denoted $w * w'$ or simply $w w'$, is the ordered tuple of $n + n'$ terms defined by:

$\map {w * w'} i := \begin{cases}

\map w i & : \text {if } 1 \le i \le n \\ \map {w'} {i - n} & : \text {if } n < i \le n + n' \end{cases}$

The word concatenation derives from the Latin com- for with/together and the Latin word catena for chain.

However, the end result of such an operation is not to be confused with a (set theoretical) chain.