Toenails
edit: I am bleary-eyed and did not utilize spell-check properly:

defiantly = definitely

pastorofmuppets
"perfect"?

kingofthenothing
"fucking convergence of a geometric series, how does it work?"

well, one-ninth is 0.111...
9 x 1/9 = 1
1=0.999...

or
x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9.0
x = 1

but you could also use geometric convergence, the series converges to .9/1-.1, or .9/.9, which equals 1.

I'm not sure what's more "perfect", as any base system is going to run into problems of infinity using real numbers. I'm just as curious as anyone else for wondering how I'd count if I were missing some fingers (or maybe grew some extra ones), but binary, base 3, octal, hex, whatever, it doesn't really change what the numbers themselves "are", just the symbols used.

pastorofmuppets
Actually I can see how the tortoise thing is more fun to think about. The .999... thing leaves you with the impression that some trick has been done with the symbols themselves.

That's not the case... as king pointed out, it's a property of infinite series rather than any particular number system, but still, Zeno's paradox gives you something a little more concrete to think about.

Fun math game: try and notice how often people fall prey to the birthday paradox or the gambler's fallacy. But don't correct them, because they will hate you for knowing some math.