# MATH Puzzle ?

Ian Goddard (igoddard@erols.com)
Tue, 28 Apr 1998 15:31:59 -0400

The binary numeric notation used by computers uses two numbers,
0 and 1, and is known as Base 2 (B2) (our traditional numeric
system is Base 10 (B10)). So what's the 1 digit of a Base 1
system, 0 or 1? The case for it being 0 and the case for
1 both seem to be equally logical. Which case is true?

Here's the "B1 digit = 1" argument based on the rule by
which we grade the value of a 1 in a given Bn column:

number
columns 3 2 1

Base 10: 10^2 10^1 10^0
100 10 1
------------------
1 1 1 = one hundred and eleven

Base 2: 2^2 2^1 2^0
4 2 1
-----------------
1 1 1 = seven

Base 1: 1^2 1^1 1^0
1 1 1
-----------------
1 1 1 = three

So this says that the B1 system assigns the value of just
1 to any 1 appearing in any column, hence 1111 = 4(B10).
Seems logical, but then here's the "B1 digit = 0" case:

B10 = 0123456789
B5 = 01234
B2 = 01
B1 = 0

And in this case we would say that Bn = (n - 1), which
is to say that in B10, the highest number is 10 - 1 = 9,
and therefore, in B1 the highest number is 1 - 1 = 0.

This case seems as logical as the opposite case for 1.

Is it that 0 (as just a placeholder) = 1? After all,
when we say "Base 2" and the two numbers of B2 are
0 and 1, we are assigning the value of 1 to the
0 and 2 to the 1... right? Is this paradoxical?
I think it's that 0 = 1 number = 1 tally mark.

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