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The Orphaned Brace

Date: 03/04/2010 at 22:40:02
From: Chris
Subject: why no closed bracket in system of equations?

When we write a system of equations, we often first write a large open
curly bracket and then write the equations in one column. One of my
students asked me why we don't close the bracket, which has got me
wondering now, too.

I've never seen a notation where that curly bracket is closed. Granted,
I know not everyone uses that same notation when writing a system of
equations, but I'm still curious.

I searched the web for my question but couldn't find any information. 
Seeing how this is a notational issue and not a procedural one, I
figured if anyone knew, it would be you guys.



Date: 03/04/2010 at 23:33:06
From: Doctor Peterson
Subject: Re: why no closed bracket in system of equations?

Hi, Chris.

I don't know that there is any "official" reason given by
whoever first used it, but here's my impression:

When we group something by using parentheses, brackets, or braces (curly
brackets), we need a pair to mark the beginning and end of the list:

  { first, second, third }

But in this usage, the single brace itself marks the beginning and the
end:

   / first equation
  |
 <   second equation
  |
   \ third equation

A second brace wouldn't add anything, so it would be a waste of the
typesetter's effort. And mathematicians have historically caused more
than enough trouble for typesetters! (Of course, the same is true of
chalk or pencil lead, and of our own time....)

The same thing is sometimes done horizontally, to mark a horizontal
grouping; and again only one is needed:

   n
  x  = 1 * x * x * ... * x
         \______  _______/
                \/
         multiply n times

I suppose if you wanted to use horizontal braces to set off a vertical
list, you would need a pair:

   ______/\______
  /              \
  first equation

  second equation

  third equation
  \______  ______/
         \/

So the difference is based on the orientation of the brace relative to
the direction of the list it groups together.

Sound reasonable?

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



Date: 03/04/2010 at 23:38:20
From: Chris
Subject: Thank you (why no closed bracket in system of equations?)

This definitely sounds reasonable! I appreciate the time you made to
answer my question.

May all your solutions be whole!

Take care,

Chris Mock
Associated Topics:
High School About Math
High School Linear Equations

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