I'm looking for a set $M$ which is partially ordered by $\subseteq$. $M$ should have a lower bound but no infimum. Is that possible?
A lower bound is an element $x \in N$ with $M \subset N$ such that for all elements $y \in M$, $x \subseteq y$ holds.
An infimum is a maximal lower bound with respect to $\subseteq$.