Talk:Trichotomy Law (Ordering)

sHi. Should the $\lor$ signs in the 3rd line of the theorem section be $\oplus$?

I think so, yes. --Lord_Farin 14:38, 16 August 2012 (UTC)

I was under the impression that $\lor$ is the main theorem, i.e. the trichotomy law, and that $\oplus$ is a related theorem that builds off it. --GFauxPas 14:45, 16 August 2012 (UTC)

Such does not conform to the definition of trichotomy (with $\lor$, also $\preceq$ will satisfy the condition). --Lord_Farin 14:55, 16 August 2012 (UTC)

This discussion is old, but there is still inconsistency between the definition of trichotomy and and the trichotomy law, without explanation of how to properly invoke these strict and weak forms. --Dfeuer (talk) 08:48, 31 January 2013 (UTC)

I can't see the inconsistency myself. It all looks good to me. --prime mover (talk) 09:12, 31 January 2013 (UTC)

Or vs. exclusive or. Good night. --Dfeuer (talk) 09:17, 31 January 2013 (UTC)

$a \prec b \not \equiv a = b$ by definition, therefore raising the non-standard and unwieldy concept of exclusive-or in the context outside the technicalities of propositional logic seems suboptimal to me.

I concede that it may be expanded and explained better, but the specifics of the proof seem sound. --prime mover (talk) 11:10, 31 January 2013 (UTC)

The problem seems to originate in the fact that the same symbol is used for multiple things whose equivalence result I have not been able to locate just yet. It's so intuitive that being rigorous can get hard. --Lord_Farin (talk) 11:15, 31 January 2013 (UTC)

Yes. This entire matter is only of concern for intuitionists (either by philosophy or more importantly by constraints of computerized proof systems). --Dfeuer (talk) 16:52, 31 January 2013 (UTC)