# The Magic of Base 3

**Wayne E Baisley**
wbaisley@enspherics.com

*Thu, 25 Oct 2001 22:18:29 -0500*

>* So, 9 * X^0 = 9 * 1 then.
*
It's not so difficult to see that positive integers raised to the zeroth
power are 1 when you think of the sequence of powers. Start with, say
1000 in base 10. Keep dividing by 10, the equivalent of reducing the
power by 1. The progression is straightforward ...
1000 = 10**3
100 = 10**2
10 = 10**1
1 = 10**0
.1 = 10**-1
.01 = 10**-2
One minor nit -- the statement "Unary notation is in a category apart
from other bases — it’s not really a positional number system ...". I'd
say it is, it's merely a degenerate case. The positions happen to be
indistinguishable.
E.g., 3 = 1 x 1^2 + 1 x 1^1 + 1 x 1^0
It's not as degenerate as base 0. ;-)
Cheers,
Wayne
You learn something wrong every day (TM).