Interval Notation

Date: 06/25/97 at 13:32:27
From: Paige Wade
Subject: Pre-Calculus (Algebra)

Can you please send me the rules for writing answers in interval 
notation?

Date: 06/28/97 at 15:21:49
From: Doctor Mark
Subject: Re: Pre-Calculus (Algebra)

Hi Paige,

First of all, interval notation always has two numbers: one on the 
left, and another on the right, separated by a comma.  (I don't want 
the Math Police to come after me, so I'd better say this also: 
infinity is not a number.) The number on the left has to be less than 
the number on the right.

If the number on either the left or the right is included in the 
interval, you use a left (if it's the number on the left) square 
bracket "[" or a right (if it's the number on the right) square 
bracket "]"

If the number is not included in the interval, you use a parenthesis 
"(" on the left and ")" on the right.

These also correspond to the inequality symbols: if it's "<" or ">" 
use a parenthesis, and if it's "<=" (less than or equal to) or ">=" 
(greater than or equal to) use a square bracket. Some examples:

If a < x <= b, you write (a, b], since a is not included in the 
interval (x has to be greater than a, so it can't equal a, and 
therefore it's not included in the interval), but b is included 
(because x could equal b).

If a <= x <= b, you write [a, b], since a and b are both included in 
the interval (x could be equal to either a or b).

If a <= x < b, you write [a, b), since a is included in the interval, 
but b isn't (x could equal a, but it can't equal b, since it is less 
than b).

If a < x < b, you write (a, b), since neither a nor b is included in 
the interval (x can't equal a because a is less than x, and x can't 
equal b because x is less than b).

Those are the only 4 possibilities. But there's a catch:

If an a or b above is infinity (or minus infinity), then you have to 
use "(" or ")" next to the infinity, since no x can equal infinity 
because infinity is not a number.  So you can never have anything like 
(- 5, infinity].

Hope this helps.  If not, write back.

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