For positive integers $n$, the subsets of the set $R$ of real numbers are defined as
$$A _ { n } = \left\{ x \in R : \frac { ( - 1 ) ^ { n } } { n } < x < \frac { 2 } { n } \right\}$$
Accordingly,
$$A _ { 1 } \cap A _ { 2 } \cap A _ { 3 }$$
the intersection set is equal to which of the following?\\
A) $\left( \frac { 1 } { 2 } , \frac { 2 } { 3 } \right)$\\
B) $\left( \frac { 1 } { 2 } , 2 \right)$\\
C) $\left( \frac { - 1 } { 3 } , \frac { 2 } { 3 } \right)$\\
D) $\left( \frac { - 1 } { 3 } , 1 \right)$\\
E) $\left( - 1 , \frac { 2 } { 3 } \right)$