Let $S$ be a set where $S$ $=$ {$1,2,3,4,5…...4444444444$} and $P$ be a subset of $S$ such that $x$ $\in$ $P$ but $2x$ $\notin$ $P$. Let $\left | T \right |$ be the total number of elements in the set $T$. Find out maximum $\left |P \right |$ of all the possible subsets $P$.