Why Do We Learn about Negative Numbers?

Date: 10/14/2004 at 11:04:29
From: john
Subject: Why do we have to learn about negative numbers.

Why do we have to learn about negative numbers?  The only context 
where I can see it being useful is in determining temperature.

My child is just being introduced to negatives and both he and I are
having difficulties with the subject.

Date: 10/14/2004 at 12:15:43
From: Doctor Ian
Subject: Re: Why do we have to learn about negative numbers.

Hi John,

Strictly speaking, there's nothing we can do with negative numbers
that we couldn't do without them.  It's just that they make some
things easier--in particular, they relieve us from having to worry
about special cases when dealing with subtraction. 

For example, suppose we're talking about longitudes.  We could always
talk about "degrees east" or "degrees west".  But then we have to have
a bunch of rules for subtracting longitudes, e.g., 

  a east - b east = (a - b) east if a > b

                  = (b - a) west if b > a

But if we just decide that east is positive and west is negative, then
we can just subtract, 

  a - b = whatever

and let the sign keep track of the direction of the result, using a
few simple rules.

But the main reason for having to learn about them is that everyone
_else_ is learning about them, and so if you don't learn about them,
you won't be able to understand what other people are talking about in
a wide variety of situations--which is kind of like moving to a
foreign country and deciding that you don't really need to learn the
language.  You can live that way, but you miss out on a lot. 

Does this make sense? 

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

Date: 10/15/2004 at 15:36:59
From: john
Subject: Thank you (Why do we have to learn about negative numbers.)

Thank you very much for your prompt and very informative answer, this
has clarified the situation for us.