Does this property have a name?

[nihili]

Here is another property my brain thought up.
Make 2 numbers, A and B.
Find the sum of these digits, F(A) and F(B).
Then make a number X that is the sum the digits of [F(A) + F(B)].

Now, with the original 2 numbers, A and B, add them together
call it C. Find the sum of the digits of C, call it Y.


Note, for any example, X=Y.
Anyone know why?

Because addition is associative.

 

[Christoph]

Because addition is associative.

That reminds me of a geek joke:
Q: What's purple and commutes?
A: an Abelian grape


IMFU, I can relate to what you're talking about. Have you ever tried taking a discrete math class? If you like this kind of stuff, you might feel right at home in discrete math. There's lots of stuff like this there.
If you want me to explain myself better, just drop me a PM. I don't mind at all.