How do you interpret the region $\sqrt{y} \leq x \leq 2$?

Question

Are the statements $i \le -1$ and $-i \le -1$ defined as false? I was trying to determine a region $D$ given by $\sqrt{y} \le x \le 2$ and wasn't sure how to interpret points like $(-1,-1)$. Is it obvious that they should be excluded? wolframalpha seems to think so.

Answer 1

To clarify, you could ask yourself what is the Domain of the square root function in this case; well, since x is a real number that must be greater than $\sqrt{y}$, this square root cannot admit negative real numbers as argument, since that would imply that $x$ would have to be greater than a complex number and that just does not make sense. Just pointing out that that the domain of your function is adapted to the problem in case, and you do want it to be $\mathbb{R}^+$.

Answer 2

Here is meant the region in the real plane. $i \le -1$ makes no sense because complex number has no order.