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In SQL the UNION clause combines the results of two SQL queries into a single table of all matching rows. The two queries must result in the same number of columns and compatible data types in order to unite. Any duplicate records are automatically removed unless UNION ALL is used.
There is an inclusion–exclusion principle for finite multisets (similar to the one for sets), stating that a finite union of finite multisets is the difference of two sums of multisets: in the first sum we consider all possible intersections of an odd number of the given multisets, while in the second sum we consider all possible ...
One common convention is to associate intersection = {: ()} with logical conjunction (and) and associate union = {: ()} with logical disjunction (or), and then transfer the precedence of these logical operators (where has precedence over ) to these set operators, thereby giving precedence over .
The relational algebra uses set union, set difference, and Cartesian product from set theory, and adds additional constraints to these operators to create new ones.. For set union and set difference, the two relations involved must be union-compatible—that is, the two relations must have the same set of attributes.
SQL allows the selection of rows from a relational table: this operation will in general yield a multiset, unless the keyword DISTINCT is used to force the rows to be all different, or the selection includes the primary (or a candidate) key. In ANSI SQL the MULTISET keyword can be used to transform a subquery into a collection expression:
The board B is any subset of the squares of a rectangular board with n rows and m columns; we think of it as the squares in which one is allowed to put a rook. The coefficient , r k ( B ) of x k in the rook polynomial R B ( x ) is the number of ways k rooks, none of which attacks another, can be arranged in the squares of B .
The listagg function, as defined in the SQL:2016 standard [2] aggregates data from multiple rows into a single concatenated string. In the entity relationship diagram , aggregation is represented as seen in Figure 1 with a rectangle around the relationship and its entities to indicate that it is being treated as an aggregate entity.
For example, the union of three sets A, B, and C contains all elements of A, all elements of B, and all elements of C, and nothing else. Thus, x is an element of A ∪ B ∪ C if and only if x is in at least one of A, B, and C. A finite union is the union of a finite number of sets; the phrase does not imply that the union set is a finite set ...