## Kitten_is_back one year ago 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

1. Kitten_is_back

i got a d

2. EmmaTassone

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

3. EmmaTassone

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.

4. EmmaTassone

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