Selection (relational algebra)

In relational algebra, a selection (sometimes called a restriction in reference to E.F. Codd's 1970 paper^[1] and not, contrary to a popular belief, to avoid confusion with SQL's use of SELECT, since Codd's article predates the existence of SQL) is a unary operation that denotes a subset of a relation.

A selection is written as ${\displaystyle \sigma _{a\theta b}(R)}$ or ${\displaystyle \sigma _{a\theta v}(R)}$ where:

• a and b are attribute names
• θ is a binary operation in the set ${\displaystyle \{\;<,\leq ,=,\neq ,\geq ,\;>\}}$
• v is a value constant
• R is a relation

The selection ${\displaystyle \sigma _{a\theta b}(R)}$ denotes all tuples in R for which θ holds between the a and the b attribute.

The selection ${\displaystyle \sigma _{a\theta v}(R)}$ denotes all tuples in R for which θ holds between the a attribute and the value v.

For an example, consider the following tables where the first table gives the relation Person, the second table gives the result of ${\displaystyle \sigma _{{\text{Age}}\geq 34}({\text{Person}})}$ and the third table gives the result of ${\displaystyle \sigma _{{\text{Age}}={\text{Weight}}}({\text{Person}})}$.

${\displaystyle {\text{Person}}}$	${\displaystyle \sigma _{{\text{Age}}\geq 34}({\text{Person}})}$	${\displaystyle \sigma _{{\text{Age}}={\text{Weight}}}({\text{Person}})}$
Name Age Weight Harry 34 80 Sally 28 64 George 29 70 Helena 54 54 Peter 34 80	Name Age Weight Harry 34 80 Helena 54 54 Peter 34 80	Name Age Weight Helena 54 54

More formally the semantics of the selection is defined as follows:

${\displaystyle \sigma _{a\theta b}(R)=\{\ t:t\in R,\ t(a)\ \theta \ t(b)\ \}}$

${\displaystyle \sigma _{a\theta v}(R)=\{\ t:t\in R,\ t(a)\ \theta \ v\ \}}$

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.