Latex practice

$$
\begin{eqnarray*}
\{x\}&=&\bigcap_{i=0}^{∞} [x,x+\frac{1}{n})\\(x,y)&=&[x,y)-\{x\}\\[x,y]&=&[x,y)+\{y\}\\(x,y]&=&[x,y)+\{y\}-\{x\}\end{eqnarray*}$$

 

$$
\begin{eqnarray*}
\{x\}&=&\bigcap_{i=0}^{∞} [x,x+\frac{1}{n})\\(x,y)&=&[x,y)-\{x\}\\ [x,y]&=&[x,y)+\{y\}\\(x,y]&=&[x,y)+\{y\}-\{x\}
\end{eqnarray*}
$$