Behind logic of Magic Number 9

Behind logic of Magic Number 9
The Magic Number 9 Reference link

Logic of this Magic
Take same Rule

1. Take an unrepeated same digit as a number. (don't take like this 2222, its make result as an infinity.)
2. Reverse that number.
3. Subtract the biggest to smallest number.
4. Now you can divide that result by 9.
(In rule 4 tells, the result exactly divide by 9, no reminders)

Proof :
1. Take Two Digit Number, 10x+y ---- (A)
2. Reverse the number, 10y+x ---- (B)
3. Assume A number is Big, so that big - small,
(10x+y) - (10y+x) = 9x-9y = 9 (x-y)
4. So it can divided by 9 without the reminders.