Selection (relational algebra)

<p>In <a href="/facts/Relational_algebra/7tjTFXdf">relational algebra</a>, a selection (sometimes called a restriction in reference to E.F. Codd's 1970 paper and <i>not</i>,  contrary to a popular belief, to avoid confusion with <a href="/facts/SQL/UjQLJcYm">SQL</a>'s use of SELECT, since Codd's article predates the existence of SQL) is a <a href="/facts/Unary_operation/kb6CkgsX">unary operation</a> that denotes a <a href="/facts/Subset/SJGERmbA">subset</a> of a relation.
</p><p>A selection is written as

σ
          
            a
            θ
            b
          
        
        (
        R
        )
      
    
    {\displaystyle \sigma _{a\theta b}(R)}
  
 or 
  
    
      
        
          σ
          
            a
            θ
            v
          
        
        (
        R
        )
      
    
    {\displaystyle \sigma _{a\theta v}(R)}
  
 where:
</p>
<ul><li>a and b are attribute names</li>
<li>θ is a <a href="/facts/Binary_operation/CYtow0bz">binary operation</a> in the set 
  
    
      
        {
        
        <
        ,
        ≤
        ,
        =
        ,
        ≠
        ,
        ≥
        ,
        
        >
        }
      
    
    {\displaystyle \{\;<,\leq ,=,\neq ,\geq ,\;>\}}
  
</li>
<li>v is a value constant</li>
<li>R is a relation</li></ul>
<p>The selection 
  
    
      
        
          σ
          
            a
            θ
            b
          
        
        (
        R
        )
      
    
    {\displaystyle \sigma _{a\theta b}(R)}
  
 denotes all <a href="/facts/Tuple/BI1HIxL8">tuples</a> in R for which θ holds between the a and the b attribute.
</p><p>The selection 
  
    
      
        
          σ
          
            a
            θ
            v
          
        
        (
        R
        )
      
    
    {\displaystyle \sigma _{a\theta v}(R)}
  
 denotes all tuples in R for which θ holds between the a attribute and the value v.
</p><p>For an example, consider the following tables where the first table gives the relation Person, the second table gives the result of 
  
    
      
        
          σ
          
            
              Age
            
            ≥
            34
          
        
        (
        
          Person
        
        )
      
    
    {\displaystyle \sigma _{{\text{Age}}\geq 34}({\text{Person}})}
  
 and the third table gives the result of  
  
    
      
        
          σ
          
            
              Age
            
            =
            
              Weight
            
          
        
        (
        
          Person
        
        )
      
    
    {\displaystyle \sigma _{{\text{Age}}={\text{Weight}}}({\text{Person}})}
  
.
</p>
<table><tbody><tr><td>                              Person                      {\displaystyle {\text{Person}}}  </td><td>                              σ                                    Age                        ≥            34                          (                  Person                )              {\displaystyle \sigma _{{\text{Age}}\geq 34}({\text{Person}})}  </td><td>                              σ                                    Age                        =                          Weight                                      (                  Person                )              {\displaystyle \sigma _{{\text{Age}}={\text{Weight}}}({\text{Person}})}  </td></tr><tr><td><table><tbody><tr><th>Name</th><th>Age</th><th>Weight</th></tr><tr><td>Harry</td><td>34</td><td>80</td></tr><tr><td>Sally</td><td>28</td><td>64</td></tr><tr><td>George</td><td>29</td><td>70</td></tr><tr><td>Helena</td><td>54</td><td>54</td></tr><tr><td>Peter</td><td>34</td><td>80</td></tr></tbody></table></td><td><table><tbody><tr><th>Name</th><th>Age</th><th>Weight</th></tr><tr><td>Harry</td><td>34</td><td>80</td></tr><tr><td>Helena</td><td>54</td><td>54</td></tr><tr><td>Peter</td><td>34</td><td>80</td></tr></tbody></table></td><td><table><tbody><tr><th>Name</th><th>Age</th><th>Weight</th></tr><tr><td>Helena</td><td>54</td><td>54</td></tr></tbody></table></td></tr></tbody></table>
<p>More formally the semantics of the selection is defined as
follows:
</p>

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

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

<p>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.
</p>

Selection (relational algebra) open-in-new

Selection (relational algebra)