Base 3

Date: 10/24/2001 at 11:09:42
From: Hannah Martin
Subject: Number systems (base 3)

What is 2+2 in base three? 

I believe it to be 4 in any number system because a one-digit number 
(x) in any base will be (x) times (the base to the zero power), or 1. 

My teacher disagrees and says that she is sure that it isn't 4.

Date: 10/24/2001 at 12:17:58
From: Doctor Peterson
Subject: Re: Number systems (base 3)

Hi, Hannah.

You have to start by distinguishing a number from a numeral (a way of 
writing a number). The sum 2+2 is always equal to the NUMBER 4; the 
only question is how to WRITE this number in base 3. In base 3, you 
count

    1, 2, 10, 11, 12, 20, 21, ...

because "11" in base 3 means 1 three and 1 one.  This, therefore, is 
how you write 4 in base 3. So the answer is, 11 (base 3).

The problem with saying that the answer is 4 is that, in base 3, there 
is no symbol 4. Similarly, I could claim that in base ten, 6 + 6 = C, 
because I am familiar with the base 16 system in which C is the digit 
for twelve. To you, C is not a digit at all, so my answer is 
meaningless to you - in base ten. I can't use C to write in base ten, 
and you can't use 4 to write in base 3.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/