# Talk:Finite Chain is Order-Isomorphic to Finite Ordinal

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It's in the category of total orderings because the restriction of an ordering to a chain is a total ordering. I think the theorem is phrased like this in Birkhoff, but I don't think he even distinguishes between a chain and a totally ordered set. I realize now I should probably prove the slightly special case of a toset first and prove this theorem from that. But first I have to figure out how I'm going to go about it. We have this result for general ordinals, but I want more elementary results for the finite case, which Birkhoff starts out with. --Dfeuer (talk) 20:24, 11 March 2013 (UTC)