Question

Which sets of numbers are closed under division?

Choose all answers that are correct.

A.
rational numbers

B.
integers

C.
{–1, 0, 1}

D.
whole numbers

Answer 1

i got a d

Answer 2

When you say whole number you mean the real numbers? Actually I think the answer is A.rational numbers and could be too D.whole number if you mean real numbers

Answer 3

I think letter B isnt right because division is not defined in integer numbers. For example:
if we take two integer numbers 2 and 3 and then we divide them \[\frac{ 2 }{ 3 }\notin \mathbb{Z}^+ and \frac{ 2 }{ 3 }\notin \mathbb{Z}^-\] So division isnt closed for integers.

Answer 4

And finally letter C is closed too (always saying that the division is not defined by zero) because every number in the set has inverse (-1,1) so division (multiplication of the inverse) is defined and closed. As you can see:
1/-1=-1
-1/1=1
1/1=1
-1/-1=1
0/1=0/-1=0