Concept explainers
(a)
To explain:
The set of irrational numbers is closed under addition or not.
(a)
Answer to Problem 32WE
The set of irrational numbers is closed under addition.
Explanation of Solution
The set of irrational numbers is closed under addition, since the sum of two irrational numbers is an irrational number.
(b)
To explain:
The set of irrational numbers is closed under multiplication or not.
(b)
Answer to Problem 32WE
The set of irrational numbers is not closed under multiplication.
Explanation of Solution
The definition of irrational numbers is:
An irrational number is a number which cannot be expressed as a fraction
Irrational numbers have decimal expansions that neither terminate nor become periodic.
Thus, from the above definition,
The set of irrational numbers is not closed under multiplication, since
Chapter 1 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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