Partition of a set, definition not clear From wikipedia:


  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?
The idea of a partition is that you take a whole (the set $X$) and you divide it to parts.

Now if I cut off an apple into slices (and one core) I have several pairwise disjoint parts of the apple, but if I reassemble the parts I get a whole apple again.

Similarly we require this from a partition of a set. We want that the union of all the parts give us the entire set we partitioned.
A collection of disjoint subsets of a given set. The union of the subsets must equal the entire original set.

For example, one possible partition of {1, 2, 3, 4, 5, 6} is {1, 3}, {2}, {4, 5, 6}.