The mysterious number 6174

Think of any 4 non-zero digits, where not all four digits are the same. Arrange the digits in descending order and ascending order and compute the difference. For instance, if the digits are 3,3,2 and 1,

3321-1233=2088

Repeat the above step by rearranging the result into ascending and descending order and compute the difference.

8820-0288=8532

Reiterating,

8532-2358=6174,

Strangely,

7641-1467=6174

The process terminates when the number reaches 6174. We can use another example,

9750-0579=9171
9711-1179=8532
8532-2358=6174

and Viola! We get the same result again! Can you figure out why this happens?