This makes it a fairly drastic assumption. I have been ignoring this point, but let's see how this works mathematically. Again, this is a very standard result. Similarly, an infinite price corresponds to a zero quantity. Maybe it's true in some cases, but it's a mistake to confuse an interesting situation with an important one.
Statisticians try to summarize what's known about demand curves.
They often find the constant-elasticity specification works better than the linear form that John seems to like. But both are approximations for some unknown form, which might be neither linear nor log-linear. I see no reason for the new terminology. This is not an issue in our discussion, so I'll ignore it. We should also remember that the firm's demand curve is also an economic abstraction.