Complete partial order

Imagine you have a big toy chest with lots of different toys inside. Some toys can be put on top of others, like stacking building blocks. We call this "being bigger" or "having more pieces."

But some toys just can't be stacked on top of others. For example, you can't stack a toy car on top of a doll because they are not the same kind of toy. We call this "not being comparable."

A complete partial order is a set of toys where we can compare any two of them. We can always say which one is bigger or smaller, or if they are the same size. And we can do this for any pair of toys in the set.

For example, if we have a set of different sized balls, we can always compare any two of them and say which one is the bigger one. And there are no two balls that can't be compared, because they are all the same kind of toy. So this set of balls is a complete partial order.

Basically, a complete partial order is a set of things where we can always compare any two of them and say which one is bigger, smaller, or if they are the same. It's like having a big toy chest full of toys we can always stack or compare, no matter what kind of toys they are.