Editing Distributive property (section)

== Definition ==

Given a [[Set (mathematics)|set]] <math>S</math> and two [[binary operator]]s <math>\,*\,</math> and <math>\,+\,</math> on <math>S,</math>
*the operation <math>\,*\,</math> is {{em|left-distributive}} over (or with respect to) <math>\,+\,</math> if, [[given any]] elements <math>x, y, \text{ and } z</math> of <math>S,</math>
<math display=block>x * (y + z) = (x * y) + (x * z);</math>
*the operation <math>\,*\,</math> is {{em|right-distributive}} over <math>\,+\,</math> if, given any elements <math>x, y, \text{ and } z</math> of <math>S,</math>
<math display=block>(y + z) * x = (y * x) + (z * x);</math> 
*and the operation <math>\,*\,</math> is {{em|distributive}} over <math>\,+\,</math> if it is left- and right-distributive.<ref>[http://mathonline.wikidot.com/distributivity-of-binary-operations Distributivity of Binary Operations] from Mathonline</ref>

When <math>\,*\,</math> is [[commutative]], the three conditions above are [[Logical equivalence|logically equivalent]].