Recent content by PeroK

I'll make this general comment for the last time. You are not thinking through these problems in terms of what you are trying to prove. Your work is superficial, IMO. It's not that you need detail, as such, but that you need to be much clearer about the steps required in the proof. In this...

It's probably a good time to move on. That's the imprecise "physicists" way of doing calculus. There are so many books that do it that way, so who am I to argue?

Although the conclusion is somewhat correct, you are falling into the trap of taking the dummy variable ##x## as inherently part of the function. Strictly speaking ##f## is the function, and not ##f(x)##. I would make a subtle change to your notation and write: $$\frac{\partial f}{\partial y}...

For a multi-variable function, you of course have to distinguish between the first and second arguments. Is ##\frac{\partial f}{\partial x}## always the partial derivative with respect to the first argument? Is that essentially a pre-defined notation?

In the quark model, electric charge is not the only elementary one. There is also color charge, which is a property of quarks, as well as other properties such isospin and strangeness etc.

It is an inherent notational problem. When you define a function ##f##, the definition is independent of the dummy variable you choose. So, for example, all these represent the same function: $$\sin x, \ \sin y, \ \sin \ \theta$$Moreover, the sine function has a well-defined derivative, which...

Do you see the close relationship between the proof of that theorem and the proof in this particular case?

You should definitely read my Insight!

That all seems fine, so I'm not sure where the problem lies. If you want a more in-depth discussion of multiple-variable partial derivatives, you could try my Insight: https://www.physicsforums.com/insights/demystifying-chain-rule-calculus/ This is a tricky question that comes up now and...

The first problem comes with the imprecise concept of "perspective". What does that even mean? It's true that light from a particular event may never reach a distant observer, but how much physical significance does that have? And, is that the only way to define your "perspective"? The short...

There's no working model of the universe with a boundary.

I'd like to see a simple proof in this case using that method. Or any proof, simple or otherwise, that isn't essentially just the ##\epsilon-\delta## we have already.

That's fine as far as it goes, but you really need a sound, logical proof. All ##\epsilon-\delta## proofs, in principle, should start with "Let ##\epsilon > 0 \dots ##".

That all looks ill-conceived to me. For example, I don't think you've corrently identified the metric that is derived from the given supremum norm. PS as pointed out in post #2.

Here's an alternative approach. Note that we must have ##a, b < 0##. As both expressions are less in this case than for the equivalent positive numbers. We can take ##c = -a, d = -b##, with ##c, d > 0## and minimise the maximum of: ##3c^2 - 2d## and ##3d^2 - 2c##. Now, for ##c, d > 0## we...