Pressure: extensive or intensive property? I know that there are already some relevant questions.
I am a physics professor and I do know that pressure is considered as an intensive property and the justification for this.
Nevertheless, I am puzzled about something I read from a book (Engineering Thermodynamics Michael Horsley, Chapman and Hall 1993).
The author has a progress type question:
"If I have some gas in a rigid container (...), is its pressure an intensive or extensive property?"
My quick answer was intensive based to the common "half the container" argument. The author's answer is (to my surprise): extensive.
Below is (in his own words) the justification:
"If (...) I let half the gas out of the cylinder, then the pressure inside the cylinder will certainly fall and the pressure of the released gas will also be quite different from its initial value. Thus the pressure is an extensive property."
What am I missing here?
 A: Intensive properties are the properties which remain constant despite varying the number of molecules $N$ and varying the amount of volume $V$ in the thermodynamic limit, i.e. where $N$ and $V$ both are large and are varied in a way that their ratio remains constant. In the example of the book you mention, $N$ is varied but $V$ is kept constant (the volume of the container) and thus, under such a scenario, an intensive property is not obliged to remain constant. 
A: Pressure is intensive. I think the way you understand extensive and intensive is a bit wrong.
An intensive property is a property which is same for any part of a system regardless of the size and shape of the part you are considering.
An extensive property is different for different parts of the system if the size is different.
In the example that the author gave, the pressure does change but still the the pressure of any part of the system you take will be same as the rest of the system regardless of the size. The pressure inside whole system has changed since it has gone through a process. After undergoing a process the intensive properties also change but the intensive property of any part of the system will be same as rest of the system at a particular time( not the same as intial value though).
EDIT ( question edited) : So I think the author's answer is wrong here.
A: Take two systems, $S_1$ and $S_2$. Let $S_{12}$ be a system obtained by putting these two together. 
A property $P$ is said to be extensive if
$$P(S_{12})=P(S_1)+P(S_2)$$
Examples: mass, volume, number of particles...
It is said to be intensive if
$$P(S_{12})\neq P(S_1)+P(S_2)$$
Examples: temperature, density, pressure...
