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Concatenation
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==Applications== ===Audio and telephony=== In programming for telephony, concatenation is used to provide dynamic audio feedback to a user. For example, in a "time of day" [[speaking clock]], concatenation is used to give the correct time by playing the appropriate recordings concatenated together. For example: "at the tone, the time will be", "eight", "thirty", "five", "and", "twenty", "five", "seconds". The recordings themselves exist separately, but playing them one after the other provides a grammatically correct sentence to the listener. 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). Programming for any kind of computerised public address system can also employ concatenation for dynamic public announcements (for example, flights in an airport). 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. ===Database theory=== One of the principles of [[relational database]] design is that the fields of data tables should reflect a single characteristic of the table's subject, which means that they should not contain concatenated strings. When concatenation is desired in a report, it should be provided at the time of running the report. 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. However, the customers data table should not use one field to store that concatenated string; rather, the concatenation of the seven fields should happen upon running the report. The reason for such principles is that without them, the entry and updating of large volumes of data becomes error-prone and labor-intensive. Separately entering the city, state, ZIP code, and nation allows data-entry validation (such as detecting an invalid state abbreviation). Then those separate items can be used for sorting or indexing the records, such as all with "Boulder" as the city name. ===Recreational mathematics=== In [[recreational mathematics]], many problems concern the properties of numbers under concatenation of their numerals in some [[radix|base]]. Examples include [[home prime]]s (primes obtained by repeatedly factoring the increasing concatenation of prime factors of a given number), [[Smarandache–Wellin number]]s (the concatenations of the first [[prime number]]s), and the [[Champernowne constant|Champernowne]] and [[Copeland–Erdős constant]]s (the real numbers formed by the decimal representations of the [[positive integers]] and the prime numbers, respectively).
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