Transitive

From CS2800 wiki
(Redirected from Transitivity)


Definition: Transitive
A binary relation [math]R [/math] on a set [math]A [/math] is transitive if for all elements [math]x [/math], [math]y [/math], and [math]z \href{/cs2800/wiki/index.php/%E2%88%88}{∈} A [/math] with [math]\href{/cs2800/wiki/index.php/XRy}{xRy} [/math] and [math]\href{/cs2800/wiki/index.php/XRy}{yRz} [/math], we also have [math]\href{/cs2800/wiki/index.php/XRy}{xRz} [/math].

In a picture, this means that every path from [math]x [/math] to [math]y [/math] has a corresponding direct edge from [math]x [/math] to [math]y [/math].