# Set difference

Definition: Set difference
If and are sets, then the set difference minus (written ) is given by .

We use the symbol instead of the normal because occasionally we will want to use sets to represent number-like things, and we will want to define subtraction differently for those sets (in particular, we will do this in the section on Category:number theory).

This means that if you know , you can conclude 'both' that 'and' , and similarly you must prove both and to prove .

In this Venn diagram, the set difference minus is shaded: