"As the number of extrema approaches infinity, so does the slope between them. An infinite slope is a discontinuity. An infinitely compressed sine wave has an infinite number of discontinuities. I just don't see how you could get around that."
Like I said, I'm not sure about my examples, but I definitely know that extrema have to be limited. It's both in my textbook and in the links. But that example still makes sense to me... for every two points in the sine wave that you infinitely compressed, there is another point between them that you also infinitely compressed and thus is still in between them. Therefore there is no discontinuity if you think about it. I may be wrong here though, I'm just relying on intuition.
"Your own links bear this out."
Check them again, a couple mention a finite number of finite discontinuities. Although on second thought I'm not sure if the discontinuities have to be finite or they're just repeating the "countably finite" definition, so you may be right there.
"What does any of this actually mean?
Can the controller not wiggle in the oppisite direction you turn it? The direction being determined by some sort of gyro. I've lost track of what you guys are arguing about, I think it started as that but now I just don't know. I suggest all parties give a simple recap of what they have said, for my sake."
Ok, here's a recap:
Rumble is possible with gyroscopes, but force feedback proper, in the sense that when you turn the gyroscope you feel a continual opposing force, is not.
The rest as far as I can make out is just a bunch of pseudointellectual pretentious bantering because the topic has no more reason to exist so we're picking apart each other's posts. What can I say, it's fun.
Nothing to see here, move along.