Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Review - Concept Check - Page 132: 3

Answer

The open interval $(a, b)$ does not include $a$ and $b$ in the interval, while the closed interval $[a, b]$ includes both $a$ and $b$ in the interval. An example of an interval that is neither open nor closed is: $(2, 4]$

Work Step by Step

The open interval $(a, b)$ means the numbers $a$ and $b$ are not included in the interval/set. As a rule, a number beside a parenthesis is not included in the interval. The closed interval $[a, b]$ means the numbers $a$ and $b$ are included in the interval/set. As a rule, a number beside a bracket is included in the interval. An interval that is neither open nor closed is one that contains both a parenthesis and a bracket. Thus, one example of an interval that is neither open nor closed is: $(2, 4]$
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