Recent content by Alesak

Ah, it's kind of obvious, now that you say it. Thank you.

What is "function of period unity"? Hi, I'm reading an article that has a sentence saying "where P is a function of period unity.". Here. I've been looking for what does it mean but without any success. Does anyone know?

You seem to be confused about what is what, such as equating scalars with operators. Why not to pick Shankar and make it clear?

google for connection between renormalization group and brain.

It got a bit messy, so let me explain. When you write f(x) ##\in ## R, it means f(x) is real number, i.e. the output from the function is a number. But when you write f(x) ##\in ## P(R), it means f(x) takes values in P(x), meaning output of f is element of P(R), meaning output of f is a subset...

You are right, a mistake.

Correct way to write it is f(x) ##\in ## P(R). If you think about it a little bit more, you will surely understand it very clearly. Read article on wikipedia about power sets, if you need. You almost got it;) The answer lies in the expression f(x) = {y ∈ R; sin y < x}. If it was...

Pretty much. More correct way to think about it is that f assigns to each x a subset of R, therefore f(x) is equal to a single element of P(R). The important concept here is that set can be taken as element of other set. Exactly. To decide between 3 and 5, notice the strict inequality in...

More appropriate mathematica example would be this: sin x < 0.5 can you show the f(0.5) on that picture?

What happens when you take power set of some set is that each subset is taken as element of P(S), where S is arbitrary set. For example, power set of S = {1, 2, 3} is {{1}, {2}, {3}, {1, 3}, {2, 3}, {1, 2, 3}}. So function from, say, R to P(x) assigns to each real number a subset of that set...

P(R) probably means power set of real numbers, meaning to each real number x it assigns a subset of real numbers. You can imagine that for each number x it assigns a set of numbers, such that sin y < x. You can imagine a plot of sine with horizontal line located at height x, and the f(x) would...

I have Geroch on my bookshelf. I haven't read it yet, but if you are algebraicaly inclined you will find it interesting.

So, if I understand it correctly, if we have time-indep potential we can use time-indep Schrödinger equation(=eigenvalue problem for Hamiltonian) to derive set of solutions for t=0, from which any other state can be formed(=they form orthonormal basis) and which can be developed into any later...

You are right, I missed this subtlety. There is also a nice article on wiki on wavefunction collapse. Some interpretations apparently doesn't require a collapse.

Screw LHC, let's do this!