Category:Well-Defined Relations

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This category contains results about Well-Defined Relations.

Let $\RR$ be an equivalence relation on $S$.

For $x \in S$, let $\eqclass x \RR$ denote the equivalence class of $x$ under $\RR$.

Let $S / \RR$ be the quotient set of $S$ determined by $\RR$.


Let $\QQ$ be a relation on $S / \RR$.


Then $\QQ$ is well-defined if and only if:

for arbitrary $x, y, x', y' \in S$ such that:
$x \mathrel \RR x'$
$y \mathrel \RR y'$
we have that:
$\tuple {\eqclass x \RR, \eqclass y \RR} \in \QQ \iff \tuple {\eqclass {x'} \RR, \eqclass {y'} \RR} \in \QQ$

Pages in category "Well-Defined Relations"

The following 2 pages are in this category, out of 2 total.