INTERVAL NOTATION
When an equation is solved, the solution set generally involves a finite set of numbers.
For example, the solution to the
equation
2
1
7
x
+
=
is the number
x
=
3
, while the solutions to the equation
x
2
1
10
+
=
are
x
= ±
3
.
When we solve an
inequality, however, the solution is usually a “connected” set of real numbers, called an interval.
Using the above examples,
the solutions to the inequality
2
1
7
x
+
>
are all numbers greater than 3, and the solutions to the inequality
x
2
1
10
+
≤
are all
numbers between or equal to
±
3
.
Interval notation provides us with some useful mathematical shorthand for representing
intervals of numbers.
Parentheses ( ) are used whenever the endpoint of an interval is not included in the solution set, and brackets [ ] are used
whenever the endpoint is included.
The symbols for positive and negative infinity,
±∞
, are used whenever an interval has
only one endpoint.
Brackets are never used on the infinite end of an interval involving the
∞
symbol, because infinity is a
concept, not a value that a variable can ever equal.
Below are some equivalent ways to represent intervals, using inequality symbols, using number lines, and using interval
notation.
Note that an open circle on a number line corresponds to a parenthesis in interval notation, while a closed circle
corresponds with a bracket.

This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Algebra, Set Theory, Bracket

Click to edit the document details