# Talk:Relation between Two Ordinals/Corollary

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What is the theorem statement of this page supposed to be? I'm not sure how the title "Relation between *Unequal* Ordinals" makes any sense for the statement $S \subseteq T$ or $T \subseteq S$; that was a mistake on my part. I subsequently "fixed" this by putting the (original) proof on the page Ordinals are Totally Ordered, but apparently there is some objection towards that approach. --abcxyz 15:50, 28 June 2012 (UTC)

- The theorem statement for this page is: if S and T are ordinals then either S is a subset of T or T is a subset of S. Where's the problem?
- Having established this elementary fact, it can then be used (in conjunction with (a) the definition of the term "total ordering" and b(b) the result (somewhere around) that the subset relation is a partial ordering, to demonstrate that ordinals are totally ordered.
- As for the page title, so rename it "Relation between Ordinals", ffs. --prime mover 16:38, 28 June 2012 (UTC)