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| {{Unreferenced|date=December 2009}}
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| In [[relational algebra]], a '''selection''' (sometimes called a '''restriction''' to avoid confusion with [[SQL]]'s use of SELECT) is a [[unary operation]] written as
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| <math>\sigma_{a \theta b}( R )</math> or <math>\sigma_{a \theta v}( R )</math> where:
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| * <math>a</math> and <math>b</math> are attribute names
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| * <math>\theta</math> is a [[binary operation]] in the set <math>\{\;<, \le, =, \ge, \;>\}</math>
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| * <math>v</math> is a value constant
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| * <math>R</math> is a relation
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| The selection <math>\sigma_{a \theta b}( R )</math> selects all those [[tuple]]s in <math>R</math> for which <math>\theta</math> holds between the <math>a</math> and the <math>b</math> attribute.
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| The selection <math>\sigma_{a \theta v}( R )</math> selects all those tuples in <math>R</math> for which <math>\theta</math> holds between the <math>a</math> attribute and the value <math>v</math>. | |
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| For an example, consider the following tables where the first table gives the relation <math>Person</math>, the second table gives the result of <math>\sigma_{Age \ge 34}( Person )</math> and the third table gives the result of <math>\sigma_{Age = Weight}( Person )</math>.
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| {| border=0 cellpadding=0 cellspacing=20 align=center
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| |- style="text-align: center"
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| | <math>Person</math>
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| | <math>\sigma_{Age \ge 34}( Person )</math>
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| | <math>\sigma_{Age = Weight}( Person )</math>
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| |- style="vertical-align: top"
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| {| border=0 cellpadding=10 cellspacing=0 style="border-collapse: collapse; border: 1px solid black"
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| |- style="background-color: silver; text-align: left"
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| ! style="border: 1px solid black" width="34%" | Name
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| ! style="border: 1px solid black" width="33%" | Age
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| ! style="border: 1px solid black" width="33%" | Weight
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| |-
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| | style="border: 1px solid black" | Harry
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| | style="border: 1px solid black" | 34
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| | style="border: 1px solid black" | 80
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| |-
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| | style="border: 1px solid black" | Sally
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| | style="border: 1px solid black" | 28
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| | style="border: 1px solid black" | 64
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| |-
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| | style="border: 1px solid black" | George
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| | style="border: 1px solid black" | 29
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| | style="border: 1px solid black" | 70
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| |-
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| | style="border: 1px solid black" | Helena
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| | style="border: 1px solid black" | 54
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| | style="border: 1px solid black" | 54
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| |-
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| | style="border: 1px solid black" | Peter
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| | style="border: 1px solid black" | 34
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| | style="border: 1px solid black" | 80
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| |}
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| |
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| {| border="0" cellspacing="0" cellpadding="10" style="border-collapse: collapse; border: 1px solid black"
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| |- style="background-color: silver; text-align: left"
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| ! style="border: 1px solid black" width="34%" | Name
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| ! style="border: 1px solid black" width="33%" | Age
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| ! style="border: 1px solid black" width="33%" | Weight
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| |-
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| | style="border: 1px solid black" | Harry
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| | style="border: 1px solid black" | 34
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| | style="border: 1px solid black" | 80
| |
| |-
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| | style="border: 1px solid black" | Helena
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| | style="border: 1px solid black" | 54
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| | style="border: 1px solid black" | 54
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| |-
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| | style="border: 1px solid black" | Peter
| |
| | style="border: 1px solid black" | 34
| |
| | style="border: 1px solid black" | 80
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| |}
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| |
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| {| border="0" cellpadding="10" cellspacing="0" style="border-collapse: collapse; border: 1px solid black"
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| |- style="background-color: silver; text-align: left"
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| ! style="border: 1px solid black" width="34%" | Name
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| ! style="border: 1px solid black" width="33%" | Age
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| ! style="border: 1px solid black" width="33%" | Weight
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| |-
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| | style="border: 1px solid black" | Helena
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| | style="border: 1px solid black" | 54
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| | style="border: 1px solid black" | 54
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| |}
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| |}
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| More formally the semantics of the selection is defined as
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| follows:
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| : <math>\sigma_{a \theta b}( R ) = \{\ t : t \in R,\ t(a) \ \theta \ t(b) \ \}</math>
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| : <math>\sigma_{a \theta v}( R ) = \{\ t : t \in R,\ t(a) \ \theta \ v \ \}</math>
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| The result of the selection is only defined if the attribute names that it mentions are in the heading of the relation that it operates upon.
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| In computer languages it is expected that any [[truth-value]]d expression be permitted as the selection condition rather than restricting it to be a simple comparison.
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| In [[SQL]], selections are performed by using <code>[[Where (SQL)|WHERE]]</code> definitions in <code>[[Select (SQL)|SELECT]]</code>, <code>[[Update (SQL)|UPDATE]]</code>, and <code>[[Delete (SQL)|DELETE]]</code> statements, but note that the selection condition can result in any of three truth values (''true'', ''false'' and ''unknown'') instead of the usual two.
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| ==See also==
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| * [[Generalized selection]]
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| ==References==
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| * http://cisnet.baruch.cuny.edu/holowczak/classes/3400/relationalalgebra/#selectionoperator
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| {{DEFAULTSORT:Selection (Relational Algebra)}}
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| [[Category:Relational algebra]]
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