two simple facts about wellfounded relations
The following are two simple facts about wellfounded relation $R$ on $X$:

1.
For each $x\in X$, $x\mathit{R\u0338}x$. (See the entry Rminimal element.)

2.
The requirement for symmetry is absent, i.e., for each $x,y\in X$, either $xRy$ or $yRx$, but not both.
Justifications for these two facts are simple. For 1, consider the subclass $\{x\}$. Then $\{x\}$ has an $R\text{minimal}$ element, which can only be $x$ itself. For 2, consider $\{x,y\}$. It has an $R\text{minimal}$ element, which is either $x$ or $y$, not both.
Fact 1 is provided here for easy reference. Keeping these two facts in mind is helpful when dealing with (proving) basic theorems about the relation^{}.
Title  two simple facts about wellfounded relations 

Canonical name  TwoSimpleFactsAboutWellfoundedRelations 
Date of creation  20130322 18:25:43 
Last modified on  20130322 18:25:43 
Owner  yesitis (13730) 
Last modified by  yesitis (13730) 
Numerical id  10 
Author  yesitis (13730) 
Entry type  Feature 
Classification  msc 03E20 