difference sets

There are two sets whose elements are overlapped partially. For example,
$A=\left\{ 1,2,3,4,5,6  \right\}$
$B=\left\{ 3,4,5,6,7,8,9  \right\}$
In preceding post as we have studied,
$A\cup B=\left\{ 1,2,3,4,5,6,7,8,9  \right\}$ .
In this case overlapped elements $\left\{ 3,4,5,6  \right\}$  become one element.

If we want to clean the overlapped elements, we use the difference set.
$A-B=A\backslash B=\left\{ 1,2  \right\}$ 
In this case the elements of $B$  $\left\{ 7,8,9 \right\}$  have no contributions to the calculation.
Note that $A-B\ne \left\{ 1,2,-7,-8,-9 \right\}$ 
Of course, $B-A=\left\{ 7,8,9 \right\}$ . We will ignore the elements $\left\{ 1,2 \right\}$ .
Hence $A\cup B=(A-B)\cup B=A\cup (B-A)$ .

These are the differences of the calculations of sets with those of real numbers.