Recent content by PeroK

That isn't the idea at all. The idea is that you can use the theorems about sequences that you will already have developed in your course to tackle the limits and continuity of functions.

It depends. Generally, it's not any easier for proving a function is continuous - because you have to consider every possible sequence. Often it will be similar to a regular epsilon-delta proof. It's quite clumsy to write down the epsilon-delta requirement for a function not to be continuous...

If you have to sit a standard analysis exam, then appealing to hyperreal numbers won't help.

An alternative, which is equivalent to the usual epsilon-delta definition is: A function ##f## is continuous at a point ##a## if for every sequence (in the domain of ##f##) that converges to ##a##, the sequence of function values converges to ##f(a)##. This is often more useful practically for...

If you want to put forward a cosmological model, then this is the sort of thing you'd be expected to produce. https://arxiv.org/pdf/2503.24263 This is what modern physics looks like.

It's a good thing it's not a crime! You'd have got five years from what I saw.

There's no easy way to say this, but your other post will be deleted by the moderators in due course. In fact, it's gone already. It seems to be common for an engineer to believe that he can push the boundaries of physics without studying the subject properly. Why this is, I don't know. In...

Good answer, but you are a dollar short here and there.

Who cares?

I have no children, thankfully!

That is useful. I didn't think this was sufficient, as we could have the odd terms and even terms both converging to different limits less than and greater than ##\varphi##. The additional equation that I thought was needed was: $$a_n - a_{n+2} = \frac{a_n^2 - a_n - 1}{a_n + 1}$$This ties the...

For most students, including myself, putting SR in this context is important. I'm quite mathematical, but diving straight into hyperbolic geometry is too abstract for me. That can come later.

Moved!

Yes, I didn't lose anything, except the time messing around.

That's what it seems like. I don't have an offline Latex editor. Is that what other people have? I've always relied on the site.