Bounded lattice

Imagine you have a bunch of different toys, but you can only play with them in certain ways. Some toys can be combined with others to make new toys, while others can't. This is kind of like a bounded lattice!

A bounded lattice is a set of things (like toys) where each thing has a relationship with every other thing. These relationships are defined by two operations: meet and join.

Meet is like taking two toys and figuring out what they have in common. You might have a toy car and a toy truck, but they both have wheels. So the meet of the car and the truck would be "wheels."

Join is like taking two toys and figuring out what they both have, even if they're different. You might have a toy bear and a toy dog, but they're both animals. So the join of the bear and the dog would be "animals."

Now imagine that you have a special toy that's called a "top" and another one called a "bottom." These toys are like the bookends that hold all the other toys together on a shelf. They're the only toys that can't be combined with anything else. This is what makes a bounded lattice "bounded" – there are two special toys that limit what you can do with all the other toys.

So a bounded lattice is like a set of toys where every toy has a way of relating to every other toy, but there are two special toys that can't be combined with anything else. These two special toys are what make everything else in the set fit together in a certain way.