Recent content by Dale

So we define ##a^x## such that holds for all real ##n## and ##m##, not just natural numbers. Then we immediately have $$1=\frac{a^x}{a^x}=a^{x-x}=a^0$$ So, your property 2 implies that ##a^0=1##. And as you said we define ##a^x## such that it obeys property 2, among others. I will also point...

Please be explicit and write it out. Usually the product rule is $$\frac{d(xy)}{dt}=x\frac{dy}{dt}+y\frac{dx}{dt}$$ but I don’t think that is what you mean here. And is that the only “laws of exponents” you intended? You used plural “laws” so I assumed there would be at least two. Perhaps you...

What are the laws of exponents that you refer to here? Please be explicit.

Umm, that is what destroys things. The tidal forces grow without bound. Any object composed of multiple fundamental particles will have some finite maximum tidal force that it can withstand before being destroyed. That structural limit will be reached before the singularity. Yes, we expect...

There is no such thing as Coriolis-only. In the rotating frame there is a centrifugal force everywhere except at the axis. The real forces plus only the Coriolis force cannot explain the motion. You can add a real force to balance the centrifugal force, but then without the centrifugal force you...

I think this is the issue I take. Just because you have a way that you prefer does not make the mainstream approach wrong. You are overstating things substantially with this. You are free to prefer a different approach and to suggest why you think it is a better approach. But saying that other...

I read the Persson and the Edward’s articles. I liked the Edward’s one. But all they are doing is making an effective gravity which includes the Newtonian gravity plus the centrifugal force. They don’t get rid of the centrifugal force, just hide it. There is nothing wrong with that. Indeed...

You can always transform to a different frame if you don’t like the centrifugal and Coriolis terms. But if you are using a rotating frame then they are not optional. Even Persson's expression still contains both the Coriolis and centrifugal terms. The only difference between his approach and...

Yes, except then.

It will never be Coriolis only. There is always the centrifugal force too. What’s the problem?

The one you linked to above? It doesn't even support your claim. Give the actual reference. If something is a matter of choice then it can be chosen. If it is a matter of choice then the most that can possibly be shown is that other choices are possible, which is already implied in the fact that...

So you start with an inertially moving object and you simply write its equation of motion in the rotating frame? Is it supposed to be just one inertial motion or is the process repeated with multiple inertial motions? Your description is very unclear. That something is “disputable” is...

What is the carousel experiment?

The nice thing about that is that having a rigorous approach to infinitesimals allows you to correct some of the errors that people make while thinking just intuitively about infinitesimals.

I think that is as it should be. Software engineers have used the title "engineer" for decades. This is one of the important things that engineers do. They take responsibility for the products they design.