Some textbooks I've seen declare inequalities such as $-2>x>2$ to have no solution, or to be ill-defined, which I disagree with. I'm curious to know if anyone else thinks the same.
Inequalities can always be written two ways. For example, $x>2$ is the same as $2
When someone interprets $-3
So when I look at an inequality such as $-2>x>2$, I take it to mean there is an implicit union behind the scenes. In other words, $-2>x>2$ and $2
Am I crazy, or is there something wrong with this interpretation?
It seems to offer some advantages. For example, it makes the solution of certain absolute value inequalities very easy and natural.