Concatenation (sets)

The concatenation is a combination of sets to form a new set. The linked set consists of all combinations of the elements of both sets using a normally non-commutative operation. The concatenation of the elements is usually used as the operation .

The concatenation is a modification of the product set operation (Cartesian product), neglecting the tuple notation. Concatenation and the Cartesian product therefore differ formally. However, since this is only a notation, the concatenation is z. B. identified in SQL with the Cartesian product.

example

The set consists of the elements , the set consists of the elements . The concatenation of both sets is therefore the set ${\ displaystyle M}$ ${\ displaystyle m_ {1}, m_ {2}, \ ldots, m_ {l}}$ ${\ displaystyle N}$ ${\ displaystyle n_ {1}, n_ {2}, \ ldots, n_ {k}}$

{\ displaystyle M \ circ N: = \ {m_ {i} \ circ n_ {j} \ mid i = 1, \ ldots, l \ wedge j = 1, \ ldots, k \}.}

Compliance with the order, d. H. and not , is essential as long as [say 'Kuller' or 'Kringel', symbol for a link in general] is not commutative. ${\ displaystyle m_ {i} \ circ n_ {j}}$ ${\ displaystyle n_ {j} \ circ m_ {i}}$ ${\ displaystyle \ circ}$

Character strings as a special case

A frequent special case is the concatenation of character strings . In this case the concatenation of the sets {'Wi', 'ki'} and {'pe', 'dia'} would result in the set {'Wipe', 'Widia', 'kipe', 'kidia'} .

Individual evidence

↑ Gottfried Vossen: Data models, database languages and database management systems. Oldenbourg Verlag, 2008, ISBN 978-3-486-27574-2 , p. 137. limited preview in Google book search
↑ Gottfried Vossen: Data models, database languages and database management systems. Oldenbourg Verlag, 2008, ISBN 978-3-486-27574-2 , p. 138. Restricted preview in the Google book search

[1] Gottfried Vossen: Data models, database languages and database management systems. Oldenbourg Verlag, 2008, ISBN 978-3-486-27574-2 , p. 137. limited preview in Google book search

[2] Gottfried Vossen: Data models, database languages and database management systems. Oldenbourg Verlag, 2008, ISBN 978-3-486-27574-2 , p. 138. Restricted preview in the Google book search