Concatenation

The strings over an alphabet, with the concatenation operation, form an associative algebraic structure with identity element the null string—a free monoid.

This technique is also used in number change announcements, voice mail systems, or most telephony applications that provide dynamic feedback to the caller (e.g. moviefone, tellme, and others).

The system would archive recorded speech of numbers, routes or airlines, destinations, times, etc.

and play them back in a specific sequence to produce a grammatically correct sentence that is announced throughout the facility.

For example, to display the physical address of a certain customer, the data might include building number, street name, building sub-unit number, city name, state/province name, postal code, and country name, e.g., "123 Fake St Apt 4, Boulder, CO 80302, USA", which combines seven fields.

In recreational mathematics, many problems concern the properties of numbers under concatenation of their numerals in some base.