CALCULUS Understanding Its Concepts and Methods

Interval

A bounded or finite
interval consists of all numbers
*x*
between two fixed numbers
*a *and
*b*.

The closed interval
[*a*, *
b*]
consists of all numbers
*x* such that
*a ≤ x ≤ b*
.

The open interval
(*a*, *
b*)
consists of all
*x* such that *
a < x < b*.

The half-open intervals are
(*a*, *
b*],
which consists of all
*x *such that
*a < x ≤ b*,
and
[*a*, *
b*),
which consists of all
*x *such that
*a ≤ x < b*
.

An interval is unbounded if at least one of
the endpoints is infinite. The unbounded intervals are of the forms
(-∞
,∞),
(-∞
,* b*),
(-∞
,* b*],
(*a*
,∞),
and
[*a*
,∞).

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.