Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Free Boolean algebra
open-in-new
<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a free Boolean algebra is a <a href="/facts/Boolean_algebra_(structure)/cHbo65jm">Boolean algebra</a> with a distinguished set of elements, called <i>generators</i>, such that: </p> <ol><li>Each element of the Boolean algebra can be expressed as a finite combination of generators, using the Boolean operations, and</li> <li>The generators are as <i>independent</i> as possible, in the sense that there are no relationships among them (again in terms of finite expressions using the Boolean operations) that do not hold in <i>every</i> Boolean algebra no matter <i>which</i> elements are chosen.</li></ol>