J.C. Hull derives the following relation $$Ke^{-rT} - S \le p \le Ke^{-rT}$$
where $p$ is european put option price, $K$ is strike price, $S$ is stock spot price,$r$ rate of interest and $T$ time to maturity. The above relation holds for no arbitrage.
The book states european put option price does not necessarily increase with increase in time to maturity. But just using the above relation as $T$ increases doesn't it mean $p$ will always go to 0 for large $T$ ?