@Matthew: it's true that an *end* in category theory is a terminal object, but it's a very very special type of terminal object in a very particular category! Generally, **'end' is not a synonym of 'terminal object'**. Likewise, 'coend' is not a synonym of 'initial object'. So in the case of your poset, you should say *terminal object* or *top element*. Probably John can explain all of this better.