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The question might appear too basic to be asked on a forum like this and the answer to the question is probably yes. But the main reason why I am asking it here is to clear the confusion in my mind after I read the book on Lattices by Davey and Priceley.

They first define chain saying for a ordered set P every x,y belonging to P, $x <y$ which is fairly good. But when it comes to anti-chain they simply add a sentence saying $x<y$ iff $x=y$ in case of anti-chain.

If none of the elements in ordered set P are related to each other why do we call P an ordered set in first place?

I referred to wolfram as well but it didn't reduce my confusion.

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 You're right to suppose that your question is not at the right level for this site. Perhaps you could try math.stackexchange.com or one of the sites mentioned in the FAQ mathoverflow.net/faq – Yemon Choi Sep 16 2010 at 16:46
(Just to give you something: perhaps you are confused about the terminology of a partially ordered set.) – Yemon Choi Sep 16 2010 at 16:46
@Yemon "MathOverflow's primary goal is for users to ask and answer research level math questions, the sorts of questions you come across when you're writing or reading articles or graduate level books." Davey and Priceley is certainly a graduate level book. – unknown (google) Sep 16 2010 at 17:25
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 I fixed some of the formatting, which had gone wrong and made your question harder to follow. Secondly, I am not convinced the book of Davey and Priestley (is her name that difficult to get right?) is a graduate-level text. Thirdly, MO is primarily meant for research-level questions; your question does not seem to be research level. – Yemon Choi Sep 16 2010 at 18:05

closed as too localized by Gjergji Zaimi, Qiaochu Yuan, Yemon Choi, François G. Dorais♦ Sep 16 2010 at 18:01

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