6
QuizMultiple Choice

Real Numbers — Quiz

Question 6 • Algebra II

Which of the following sets is closed under division?

Answer
A
natural numbers
B
non-zero rational numbers
C
irrational numbers
D
non-zero integers

Explanation

A set is closed under division if dividing any two members (with a nonzero divisor) always gives another member of the set. The quotient of two non-zero rational numbers is rational and non-zero, so it remains in the set. For example, non-zero integers are not closed under division because 1 ÷ 2 = 1/2 is not an integer.

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