Definition talk:Strict Total Ordering

It should be defined with trichotomy -- with this definition instead $x \prec y \lor x = y \lor y \prec x$

Basically - you are then asserting $x \prec y \lor y \prec x$ but you are requiring that x and y be distinct elements.

Here is why - with the current definition, assume we have a nonempty $A$ st $\prec$ is a strict total ordering. Because it is nonempty, $A$ must contain at least one $x$. So $\exists x: x \in A$, so $\neg x \prec x$. Because $\neg x \prec x \land \neg x \prec x$, $\neg ( x \prec x \lor x \prec x )$ which contradicts the fact that the structure $( A, \prec )$ is a strict total ordering. --asalmon


 * Good call. In order to emphasise the fact that the ordering is strict I have structured the statement in the way you see. --prime mover 12:23, 25 November 2011 (CST)