Five, try to select 1999 integers from the set $\{1,2,3, \cdots, 3000\}$ to form a subset $A$, such that if $x \in A$, then $2 x \notin A$.
Five, the selection method is as follows:
1) Select 1500 integers from 1501 to 3000 to form $A_{1}$.
2) From 1 to 1500, remove numbers 751 to 1500 (these numbers multiplied by 2 are in $A_{1}$), and select 376 to 750, a total of 375 integers to form $A_{2}$.
3) From 1 to 375, remove 188 to 375 (these numbers multiplied by 2 are in $A_{2}$), and select 94 to 187 from 1 to 187, a total of 94 integers to form $A_{3}$.
4) From 1 to 93, remove 47 to 93 (these numbers multiplied by 2 are in $A_{3}$), and select 24 to 46 from 1 to 46, a total of 23 integers to form $A_{4}$.
5) From 1 to 23, remove 12 to 23 and select 6 to 11 and 1 (or 2), a total of 7 integers to form $A_{5}$.

Let $A=A_{1} \cup A_{2} \cup A_{3} \cup A_{4} \cup A_{5}$, then the number of elements in $A$ is: $1500+375+94+23+7$ $=1999$ (elements).