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### 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?
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```
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/
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Associated Topics:
Elementary Math History/Biography