Interval Notation for the Number Line

Date: 03/04/2009 at 20:02:08
From: Lavern
Subject: what does the graph of the interval [-4,10] look like

What does the graph of the interval [-4,10] look like?  I have no
clue.  All of Algebra is confusing.

Date: 03/04/2009 at 23:12:10
From: Doctor Peterson
Subject: Re: what does the graph of the interval [-4,10] look like

Hi, Lavern.

Interval notation is a way to identify a segment of a number line very
compactly, by essentially boiling the graph itself down to its 
essentials.

Take this interval as an example:

                 o===========================*
  <--+---+---+---+---+---+---+---+---+---+---+---+---+-->
    -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6

Here I'm using "o" to represent an open dot that shows that a number
at the end is NOT included in the set, and "*" for a closed (solid)
dot that shows the end point IS included in the set.  As an inequality
this can be written as

  -3 < x <= 4  (-3 is less than x, and x is less than or equal to 4)

Another way to draw the graph is to use a rounded parenthesis, "(" or
")" at a non-included endpoint, and a square bracket, "[" or "]", at
an included endpoint:

                 (===========================]
  <--+---+---+---+---+---+---+---+---+---+---+---+---+-->
    -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6

Interval notation is just a collapsed version of this form of graph.
We first write the end indicator on the left, "("; then the value on
the number line at that point, "-3", then, after a comma, the value on
the right, "4", followed by the end indicator on the right, "]":

  (-3, 4]

Thus this brief symbol says

  All numbers between -3 and 4, not including -3 but including 4.

Your example has square brackets at both ends, so both -4 and 10 are
included in the interval; so you'll draw a line from -4 to 10 and use
the end indicators (solid dots or brackets) that you have been taught
to use in that case.

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


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