wellfounded relation
A binary relation^{} $R$ on a class (http://planetmath.org/Class) $X$ is wellfounded if and only if

•
each nonempty subclass of $X$ contains an $R$minimal element and,

•
for each $x\in X$, $\{y\mid yRx\}$ is a set.
The notion of a wellfounded relation is a generalization^{} of that of a wellordering relation^{}: proof by induction and definition by recursion may be carried out over wellfounded relations.
Title  wellfounded relation 

Canonical name  WellfoundedRelation 
Date of creation  20130322 17:24:31 
Last modified on  20130322 17:24:31 
Owner  ratboy (4018) 
Last modified by  ratboy (4018) 
Numerical id  9 
Author  ratboy (4018) 
Entry type  Definition 
Classification  msc 03E20 
Related topic  Relation 
Related topic  RMinimalElement 
Defines  wellfounded 