Algebraic Explanation of the magical 1089 prowess

Concerning our Magic Number of yesterday 1089; Using non palindromic numbers to perform operations and still be getting 1089. The explanation is as shown below:

• If we let x, y, z denote the three digits of the original number, 
• then the three-digit number is 100x+10y+z.
•  The reverse will be 100z+10y+x. 
• Subtract: (100x+10y+z)-(100z+10y+x) to get 99(x-z). 
• Since the digits were decreasing, (x-z) is at least 2 and not greater than 9,
•  Therefore the result must be one of 198, 297, 396, 495, 594, 693, 792, or 891.
•  When you add any one of those numbers to the reverse of itself, you get 1089!

• Check it out!