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.