Proof of a viewer's comment

       In my post  '11', I received a comment from
Anjana, who stated an interesting property
of the number 9 :

       If you pick a 2-digit number, reverse the 
digits, and subtract the smaller number 
from the bigger number, you get a multiple 
of 9.

      I believe that I can explain this, using a
method I worked out :

Step 1 : Start with any number. [Not necessarily a 2-digit number.]
Step 2 : Add up its digits.
Step 3 : Is the result a one-digit number ?
             If no, see step 2.
             If yes, continue.
Step 4 : This will be its digit root or DR.

      Now to start with the property :
The number stated will have a digit root
of 'x'.
        Re-arranging the digits does no difference to the
DR, so the second number will also have DR 'x'
Subtracting one number from the other in any order,
will be x - x = 0.
       Look at fact 1. So the DR of the difference is also 9.
Since the divisibility of 9  requires a number's Digital Root
to be 9, the difference is divisible by 9.
        Thus proved.