Intensive and extensive properties of gases Every chemistry textbook I have ever seen defines intensive and extensive properties the same way: Intensive properties are those which do not depend on how much matter is present, while extensive properties do. I came across a question while looking through sample FE exam questions for which my understanding of these properties by this definition failed. The gist of my question really just revolves around pressure and volume in largely compressible substances (i.e., gases).

It seems that, when considering a gaseous substance, these definitions are not robust enough:


Volume can be shown to be independent of the amount of material present by simply compressing the gas.
Density can be shown to be dependent on the amount of material present by keeping a fixed volume and simply adding more gas molecules.


While I have heard the convincing argument that we should simply consider smaller subsets of the original to determine intensiveness and extensiveness (for instance, if I consider half of the container instead, the volume halves from $V_0$ to $\frac{1}{2}V_0$ and the density remains constant at $\rho$), this doesn't help me to identify why the conventional definition remains in use with what seems like flawed implications. Can anyone help to clarify this?
To give you a more clear explanation of the definition of these properties, it's more easy to remember them this way :

-Extensive properties are those which *are additive * ( mass, volume ) for example 1 L + 1 L = 2 L. On the other hand, intensive properties are not additive ( temperature, pressure, concentration ) for example 2 mol/L + 3 mol/ L does not give you a 5 mol/L solution. These are properties which don't change at any circumstance.

Some other thing to be considered :
The ratio of two extensive properties, gives us an intensive property. For example density= mass/volume. Since it is a ratio it will always be the same regardless of how much of a sample is measured.