Defunkt is right. I do not understand Fernando's proof. As far as I can tell, it assumes what we are trying to prove.

No, it doesn't
It does

__not__ prove that every point of e^ik is a limit point.

Why do you think this is what was to be proven? And "a limit point"...of __what__??
Furthermore, the existence of

**a** limit point, which Bolzano Weirstrass shows, does not prove that every point of e^ik is a limit point.

It also does not prove that Saturn has more than 15 satellites...I think you didn't even understand what was to be proved.
The problem is straight-forward. I do not consider an obscure theorem in obscure symbolism "help."

The problem was obviously not that straightforward for you as you apparently

didn't even understand what had to be proved.

Certainly that Jacobi's theorem may be not that well-known, but its symbolism is completely

standard and its difficulty rather medium/low for anyone with 2-3 years of undergraduate studies in maths.
I consider that a game.

Much of mathematics is a game: a rather wonderful, intelectually challenging and

mind-absorbing game. What with this?
By the way, I couldn't solve it.

After you belittled someone who tried to help __and__ in the same instance you

claimed you did prove it? Well, go figure...
If someone wants to help, this is what I would cosider help:

Given any point at angle alpha <= 2pi on the unit circle. What are k and n st:

k-n2pi-alpha < epsilon

You surely meant: "Given any ....etc", and this is __exactly__ what the proof

presented by Fernando did
An intelligible algebraic solution is sought.

It has been given already, both by Fernando and by myself, at least. That __you__ didn't understand

them is , perhaps, deplorable and sad, but you could have asked for further explanations.

Instead, you chose to behave in an even more deplorable way.

Tonio
I'll start it as a thread since this one is hopelessly cluttered.