Math problem that is driving the Internet crazy

[polymath257]

It's called modular arithmetic base 9. This works because the remainder when you divide 10 (the base of our number system) by 9, is 1.

There are a lot of 'magic tricks' that are based on this.

You can do similar thing with multiplication by 5 to get 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1,... Notice that these are your sequence with order reversed.

Or multiply by 7 each time: 7, 2, 5, 8, 2, 5, 8, ... Note that these are every other one from the previous.

Or you can take any two numbers, say 384 and 927. Multiply them to get 355968. Now, "reduce all by 9's": 384=15=6 and 927=18=9. Now, 6*9=54=9.
But, 355968=3+5+5+9+6+8=36->3+6=9, the same answer. And you will always get the same answer (but not always 9).

Thank God I'm not the only one playing with these toys! Shall we go into fractal geometry!? There is just something about infinity that is so damned appealing!

I'd point out that 9 is only important here because we work in base 10=9+1. If we worked in base 16, then 15 would be the relevant number.

Fractal geometry? Sure. But a LOT of the popular stuff out there is more 'gee whiz' than actual math. Once you get to the concept of a fractional dimension for a metric space, we have something to talk about.

And if you want to talk about 'infinity', I'd suggest learning some set theory first.