Set of positive integers
Solution 1:
The set $A:=\{2^k:\ k\geq11\}$ is infinite and has the desired properties, so there is no maximum number of elements that $A$ can have.
The set $A:=\{2^k:\ k\geq11\}$ is infinite and has the desired properties, so there is no maximum number of elements that $A$ can have.