Kaprekar Routine

Start with any whole number (but it should have more than one digit. Four digits works well.) I'll start with 5820. Make a new number by writing the digits in descending order:
8520
and another by writing them in ascending order:
0258 = 258
Now subtract the two:
8520-258 = 8262
This process is called the Kaprekar routine. Notice that you start with one number and end up with a new number. From there you can repeat the process if you wish.
Here's the sequence I get:
8520 -> 8262 -> 6354 -> 3087 -> 8325 -> etc.
If you continue long enough what do you notice?

Source: Wolfram MathWorld:Kaprekar Routine