How to express that one interval is included in another interval?

Question

Would the symbol "$\in$" work for denoting that one interval is included in another interval? Like this:

$(x>2) \in (x>0)$

Answer 1

No, it wouldn't; $x \in y$ denotes that $x$ is an element of the set $y$. What you want is to denote that an interval $i$ is a subset of another interval $j$. The notation for this is $i \subseteq j$. ($i \subset j$ denotes that $i$ is a "proper" subset of $j$, meaning that $i \neq j$.)

Answer 2

As explained by DylanSp and Paolo the right relation would be inclusion, not pertenence but in addition the way you expressed those intervals is wrong, they should be: $$(2,\infty) \ \subset \ (0,\infty) $$ or $$\lbrace x|x>2 \rbrace \subset \lbrace x|x>0 \rbrace$$

Added: I'm using the convention that the symbol $\subset$ denotes the non-strict inclusion but both conventions are frequently used.