PeroK's latest activity

That's why i checked about the AC. Think about how awkward it is to get a bijection between ##\mathbb R## and ##\mathbb R^2##.

I suspect the proof is non trivial!

Does that work?

That is the issue. Many people, for whatever reasons, believe that the universe must be fundamentally deterministic. QM challenges that...

I recommend correcting the thread title! I assumed someone would have done it by now.

Is this what you are looking for? https://en.m.wikipedia.org/wiki/Elastic_pendulum

I looked it up. The AC is not needed.

For example, ##X = Y = \mathbb R## and ##f = g## are both the exponential function. Then how to construct ##F##?

You can construct Maxwell's equations in non-orthogonal coordinates if you like. Then you'll get a non-isotropic speed. As always, this...

This made me laugh: Linux has been using SSH for decades with that same principle, securing practically all the servers of the...

That's one representation of Minkowski geometry, where the vertical axis is time and the horizontal axis is spatial. The spacetime...

The proportional of the total time that ##v_1## applies is ##\frac{v_2}{v_1+v_2}##. This is a relative weighing of ##v_2##. And vice versa.

In statistical thermodynamics, the following approximation is frequently used: $$\ln{(n!)}=\ln(1)+\ln(2)...\ln(n-1)+\ln(n)\approx...

$$\bar{v}=\frac{2L}{L/v_1+L/v_2}=\frac{2v_1v_2}{v_1+v_2}$$ I am not sure what are harmonic mean and weighted average you say in this result.

Here it is tacitly assumed that ##x\gg n##. Under this approximation $$x(x-1)(x-2)....(x-(n-1)) \approx x^n$$