Why is a UNION operation independent in relational algebra? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T07:29:33Z http://mathoverflow.net/feeds/question/112004 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/112004/why-is-a-union-operation-independent-in-relational-algebra Why is a UNION operation independent in relational algebra? mariuszmm3 2012-11-10T17:49:15Z 2012-11-12T06:26:06Z <p>Why is a set union operation independent in relational algebra? Why it cannot by expressed by the other four basic operations (selection, projection, cartesian product and difference)? What kind of queries require set union?</p> http://mathoverflow.net/questions/112004/why-is-a-union-operation-independent-in-relational-algebra/112148#112148 Answer by Carl Feynman for Why is a UNION operation independent in relational algebra? Carl Feynman 2012-11-12T06:26:06Z 2012-11-12T06:26:06Z <p>The other operations you list all have the property that they cannot map two values appearing in different columns of their input relations into the same column. Clearly this property is preserved by function composition. But UNION does allow mapping values into the same column, so it cannot be constucted by compositions of the other operations.</p>