Recent content by meiji1

Homework Statement Consider a rigid sphere of radius 1 and center at (0,0,0) that rotates about its center. The angular velocity is $\omega(t) = (\cos(t) , \sin(t), \sqrt(3))$. Does the path of the point starting at (0,0,1) ever reach this point at a later time? Homework Equations...

I mean that you should consider division of n by primes, yes.

That's not quite a contradiction. You've assumed the statement is true in the subcase that n \ge 3, in which the statement "2^(1/2) is an integer" has no effect. Maybe go up to a^n=n•b^n, and look at primes dividing n on the RHS.

The fact that 2^n > n means that n cannot have n or more prime factors. Supposing that a and b are coprime also helps.

I've got it now. It's very clear to me. Thanks very much. :)

No, I was not successful. I wish I'd thought of the counterexample you gave. Thanks for the hint. I'll give it some thought and report back. :D

I made a mistake in the problem statement. I apologize - I meant transcendental over F_E.

Well, an extension E is algebraically closed if all zeros of E[x] are contained in E. By minimal polynomial, do you mean the irreducible polynomial of \alpha over F? It's not supposed at the outset that \alpha is algebraic over F.

Homework Statement Let E be an extension field of a field F. Given \alpha\in E, show that, if \alpha\notin F_E, then \alpha is transcendental over F_E. Homework Equations F_E denotes the algebraic closure of F in its extension field E. The Attempt at a Solution First, I assumed \alpha...