SOLUTION: Which of the following list of numbers is closed under division? A. Rational Numbers B. Whole Numbers C. Perfect Squares D. Irrational Numbers

Question 1164345: Which of the following list of numbers is closed under division? A. Rational Numbers B. Whole Numbers C. Perfect Squares D. Irrational Numbers
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Take any two rational numbers and divide one by the other. Do you always get another rational number?

Hint: Let

, and

be integers. Then

and

are rational numbers by definition.

Now you have to decide whether

and

are integers or not. If they are, then

is rational and the rationals are closed under division, otherwise not.

Take any two whole numbers and divide one by the other. Do you always get another whole number?

Even though it doesn't make any difference for this particular question, I refuse to answer any question using the term "whole numbers" unless you define the term. Some define the Whole Numbers as the positive Integers equivalent to one definition of the Natural Numbers. Some define the set as the non-negative Integers equivalent to the other definition of the Natural Numbers. And some define the Whole Numbers as equivalent to the complete set of Integers.

Take any two perfect squares and divide one by the other. Do you always get another perfect square?

Hint: Divide 4 by 25.

Take any two irrational numbers and divide one by the other. Do you always get another irrational number?

Hint:

John

My calculator said it, I believe it, that settles it

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