You've got to start with the ideal gas law
Where, in this version, $m$ is the mass of the gas, $R$ is the specific gas constant and $T$ is the temperature. If $m$ and $T$ are constant, then $mRT$ = constant = $C$.
It is important to note that Boyle's law only applies to a closed system, i.e., a system where $m$ is constant. So even if the volume increases there are always the same number of gas molecules within that volume. Although the density of the gas (molecules per unit volume) keeps decreasing with increasing volume, it never becomes zero. And as long as there are gas molecules, there will be collisions between the molecules and any surfaces within or bounding that volume resulting in pressure proportional to the collision rate.
So if the volume were infinite, it would simply mean that an infinite amount of time would be required for a collision to occur. The rate of collisions approaches zero, but can never actually become zero as long as there are gas molecules in the volume.
Hope this helps.