1. ## Sets and Logic

{ x l x e R and 0 < x < 2}
{1,2}

The book says these two sets aren't equal but I don't understand why not.

2. The set $\left\{ {x:x \in \Re \wedge 0 < x \leqslant 2} \right\}$ is the set of all real numbers that a greater than 0 but less than or equal to 2.
Whereas, $\left\{ {0,2} \right\}$ is a set with only two elements, 0 & 2.
Do you see why it is impossible that they could be equal?

3. No, because the second set contains the numbers one and two, not zero and two. One is greater than zero but less than two. And two is greater than zero and equal to two. Shouldn't that make them equal?

4. The first set contains $\sqrt{2}$. The second one does not.