# How many elements are in the following set?

The set is $$\{ x \in Q:x^2 =64/25 \}$$

I thought the answer was $\{ \frac{8}{5}, -\frac{8}{5} \}$ but I am told there are in fact 4 distinct elements:

$$\{ \frac{8}{5}, \frac{8}{-5}, \frac{-8}{5}, \frac{-8}{-5}, \}$$

So are there 2 elements in the set or 4?

• Unless the question is worded strangely, your answer was right. The second and fourth elements there are usually omitted in every form of arithmetic I've ever used (since they're equivalent). – co9olguy Mar 30 '15 at 17:49
• What is $Q$? Just the set of rational numbers? It it's some kind of set $\{(a, b): a, b \in \Bbb Z\}$ and each pair gets identified with a sort of formal fraction $\frac{a}{b}$ but without the equivalence relation we put on $\Bbb Q$, then I could see $4$ elements. – pjs36 Mar 30 '15 at 17:52
• Q is $\mathbb{Q}$ – Greg Mar 30 '15 at 18:10