Plus and Minus Signs

Date: 08/14/2002 at 17:38:32
From: Ozgur Cobanoglu
Subject: Plus or minus sign '±'

I came across two signs while I was trying to do something with 
Microsoft Equation Editor. One of them is ± and in the other one the  
minus is over the plus sign. There must be a difference because there 
are two different signs. I have heard that one of them comes from  
ancient Egypt, but I don't know which.

I want to learn their history and the difference in usage.

Thank you.

Date: 08/14/2002 at 22:43:19
From: Doctor Peterson
Subject: Re: Plus or minus sign '±'

Hi, Ozgur.

We usually use the plus-or-minus sign, with the plus on top, when we 
want to indicate that both signs are valid. The classic example is in 
the quadratic formula, where each choice of sign for the square root 
leads to a different root.

In some cases there will be two places in an equation (or set of 
equations) where a choice of sign is needed, and the choice is 
linked. If when one is chosen as positive the other is to be 
negative, we use a minus-or-plus sign for the second. This indicates 
that we choose either the top sign in both plases, or the bottom sign 
in both places. This is illustrated here in Eric Weisstein's 
MathWorld:

   http://mathworld.wolfram.com/PlusorMinus.html 

As for its origin, Jeff Miller's page

   Earliest Uses of Symbols of Operation
   http://jeff560.tripod.com/operation.html 

says

    Plus-or-minus symbol (±) was used by William Oughtred
    (1574-1660) in Clavis Mathematicae, published in 1631
    (Cajori vol. 1, page 245).

There may have been a similar symbol in Egypt, but it certainly would 
not have had this meaning.

If you have any further questions, feel free to write back.

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