Equivalently, a set P is a partition of X if, and only if, it does not contain the empty set and:
- The union of the elements of P is equal to X. (The elements of P are said to cover X.)
- The intersection of any two distinct elements of P is empty. (We say the elements of P are pairwise disjoint.)
I clearly understand that the intersection between partition is empty (point 2), but how can the union of a partition can be the all elements in the set?
If it is a partition, shouldnt they be just a part?
I imagine a set divided in 3 and the elements in the first part are not all the elements of the second part.
How do you explain this?