Which statement is false? A. every irrational number is also a real number. B. every integer is also a real number. C. no irrational number is irrational. D. every integer is also an irrational number.

Question
Irrational numbers
asked 2021-02-21
Which statement is false?
A. every irrational number is also a real number.
B. every integer is also a real number.
C. no irrational number is irrational.
D. every integer is also an irrational number.

Answers (1)

2021-02-22
The set of real numbers include integers, rational numbers, and irrational numbers. This then implies that all irrational numbers and integers are also real numbers and thus statement A and B are correct.
The rational numbers are all numbers that can be written as the division of two integers, which thus also include all integers. The set of irrational numbers then contains all real numbers that are NOT rational numbers and thus the set of irrational numbers do not include integers, which implies that statement D is false.
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