Transitivity
Transitivity
Südliche Weinstraße
<ul> <li> In <a href="Grammar">Grammar</a>, a verb is <b>transitive</b> if it takes an object. See <a href="Transitive verb">Transitive verb</a>. </ul><ul><li> In <a href="Logic">Logic</a> and <a href="Mathematics">Mathematics</a>, a <a href="Binary relation">Binary relation</a> <i>R</i> is <b>transitive</b> if <i>xRy</i> and <i>yRz</i> together imply <i>xRz</i>. For example, the <i>less-than</i> relation is transitive. See <a href="Transitive relation">Transitive relation</a>, <a href="Intransitivity">Intransitivity</a>. </ul><ul><li> In <a href="Mathematics">Mathematics</a>, a <a href="Group action">Group action</a> is <b>transitive</b> if it has just one <a href="Group action">orbit</a>. It is called <b>doubly transitive</b> if it is transitive on ordered pairs of distinct elements, and so on for <b>triply transitive</b>, etc. An <a href="Ergodic theory">ergodic</a> group action is also called <i>metrically transitive</i>. </ul><ul><li> In <a href="Set theory">Set theory</a>, a set is <b>transitive</b> if it contains all <a href="Element (mathematics)">elements</a> of its elements. See <a href="Transitive set">Transitive set</a>. </ul><ul><li> <a href="Transitive Corporation">Transitive Corporation</a> is a <a href="Computer software">Computer software</a> firm based in <a href="Manchester">Manchester, England</a> and <a href="Los Gatos, California">Los Gatos</a>, <a href="California">California</a>. </ul>