  We explicitly prove that the transfer matrix of a finite layered
$PT$-symmetric system of fix length $L$ consisting of $N$ units of the
potential system `$+iV$' and `$-iV$' of equal thickness becomes a unit matrix
in the limit $N \rightarrow \infty$. This result is true for waves of arbitrary
wave vector $k$. This shows that in this limit, the transmission coefficient is
always unity while the reflection amplitude is zero for all waves traversing
this length $L$. Therefore, a free space of finite length $L$ can be
represented as a $PT$-symmetric medium.
