Int(E) mean ? what does Int mean In real analysis what is Int symbol mean?
like  Int(E) , int (A U B) ??
I want to know what is Int mean in real analysis 
a few example will be also good 
thank you 
 A: int $A$ means set of all interior points of $A\subseteq\mathbb{R}$
for example say $A=\mathbb{Q}$, Then int $A=\emptyset$
$A=[0,1]$, Then int $A=(0,1)$
A: $\operatorname{int}E$ is the set of all interior points in $E\subseteq\mathbb{R}$. Recall that a point $p$ is an interior point of $E$ if  $B_\epsilon p\subset E$. (where $B_\epsilon p$ denotes the open ball with radius $\epsilon$, centered at $p$.)
Also, note that an open set $E$ is where all the points are interior.
A: In general topology (which construction works also in metric spaces), the interior of a set $E$ is the union of all open sets contained in it. Equivalently, it is the greatest open set that is still contained in $E$. Formally, $$\operatorname{int}\,(E)=\bigcup_{\substack{U\text{ is open}\\U\subseteq E}}U.$$
Examples in the Euclidean space of the reals:
\begin{align*}
\operatorname{int}\,(E)=&\,E\qquad\text{for any open $E\subseteq\mathbb R$},\\
\operatorname{int}\,([0,1])=&\,(0,1),\\
\operatorname{int}\,([0,1))=&\,(0,1),\\
\operatorname{int}\,(\{x\})=&\,\varnothing\qquad\text{for any $x\in\mathbb R$},\\
\operatorname{int}\,(F)=&\,\varnothing\qquad\text{for any finite set $F\subset\mathbb R$},\\
\operatorname{int}\,(C)=&\,\varnothing\qquad\text{for any countably infinite set $C\subset\mathbb R$}.
\end{align*}
The last point implies, perhaps surprisingly, that if $\mathbb Q$ is the set of rational numbers, then
\begin{align*}
\operatorname{int}\,(\mathbb Q)=\varnothing.
\end{align*}
Even more surprisingly,
\begin{align*}
\operatorname{int}\,(\mathbb I)=\varnothing,
\end{align*}
where $\mathbb I$ is the set of irrational numbers.
