Editing Relational algebra (section)

== Set operators ==
{{main|Set theory}}
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 [[relation (database)|relation]]s involved must be ''union-compatible''—that is, the two relations must have the same set of attributes.  Because [[set intersection]] is defined in terms of set union and set difference, the two relations involved in set intersection must also be union-compatible.

For the Cartesian product to be defined, the two relations involved must have disjoint headers—that is, they must not have a common attribute name.

In addition, the Cartesian product is defined differently from the one in [[Set (mathematics)|set]] theory in the sense that tuples are considered to be "shallow" for the purposes of the operation.  That is, the Cartesian product of a set of ''n''-tuples with a set of ''m''-tuples yields a set of "flattened" {{math|(''n''&nbsp;+&nbsp;''m'')}}-tuples (whereas basic set theory would have prescribed a set of 2-tuples, each containing an ''n''-tuple and an ''m''-tuple).   More formally, ''R'' × ''S'' is defined as follows:

<math display=block>R\times S:=\{(r_1,r_2,\dots,r_n,s_1,s_2,\dots,s_m)|(r_1,r_2,\dots,r_n)\in R, (s_1,s_2,\dots,s_m)\in S\}</math>

The cardinality of the Cartesian product is the product of the cardinalities of its factors, that is, |''R'' × ''S''| = |''R''| × |''S''|.