One Plus One

Date: 04/11/97 at 23:15:49
From: Terra James
Subject: One plus one

Are you sure that 1 plus 1 equals 2?

Date: 04/12/97 at 16:23:36
From: Doctor Mason
Subject: Re: basic Math

Terra, though I wonder if you composed your question tongue-in-cheek, 
it is actually a very good one.  The answer is, "It depends."  It 
depends on the understood base of operation; it depends on an acquired 
level of abstraction, and it depends on meaning of symbols and 
vocabulary.  If you can find a course in the history of numbers, this 
would probably be one of the topics of discussion.  We spend several 
weeks on this subject in a course I teach. 

However, to summarize briefly, 1 + 1 = 10 in base 2 since 2 is not a 
base 2 digit.  In base 2, 10 represents 1 group of 2's and 0 ones.  
(This is what is known as a binary number.  The prefix bi- means 2.)

Consider our many words for two in English: pair of shoes, brace of 
partridges, yoke of oxen, etc.  This indicates that originally the 
concept of "two" was linked to the object one was counting.  "1" and 
"2" are arbitrary symbols which eventually developed to hold the 
meaning we know for them.  It is not unlikely that they could have 
developed different meanings, or may have developed different meanings 
in other cultures.

-Doctor Mason,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/