Take the 2-minute tour ×  Exercise 1.2.8 (Part 1), p.8, from
Categories for Types by Roy L. Crole  Definition: Let $X$ be a
preordered set and $A \subseteq X$. A join of $A$, if such
exists, is a least element in the set of upper bounds for $A$. A
meet of $A$, if such exists, is a greatest element in the set of
lower bounds for $A$.  Exercise: Make sure you understand the
definition of meet and join in a preorder $X$. Think of some
simple finite preordered sets in which meets and joins do not
exist.  share|improve this question You should know that whilst
it's perfectly okay to ask and answer your own questions here,
you should do it in a way which improves the overall quality of
the site. It's not completely clear that posting and answering
textbook exercises does that. By all means, carry on - but
perhaps try to keep the frequency down. If you post a lot of
questions, they take up room on the front page, and other
questions will get pushed down. –  Chris Taylor Jul 23 '12 at
17:34 @ChrisTaylor Thanks for th