Guys I am struggling to understand the lattice concept:
Could you help me with this silly example?
Take the collection $\{\emptyset, \{0\}, \{1\}\}$ ordered by inclusion. This is a poset, but not a lattice since $\{0\}$ and $\{1\}$ have no common upper bound.
Why this is not a lattice?
This is the definition of lattice:
So if I take $\{0\}$ and $\{1\}$ I have to show that the join and the meet belongs to X, right?
join $= \{0\} \vee \{1\} = {1}$ wich belongs to X. And meet$=\{0\} \wedge \{1\} = {0}$ wich belongs to X
What am I missing?
Many thanks!