Recent content by mufq15

For anyone keeping score at home, I think the irreducible case is also by induction. Consider an intermediate field made by adjoining a root r of f to K, and then consider L as a splitting field over K(r) of g(x) (where f(x) = (x - r)g(x).)

Homework Statement Let f in K[x] be a polynomial over a field K. Define the notion of a splitting field L of f over K. Show that if deg f = d, then f has a splitting field over K of degree dividing d! The Attempt at a Solution If f is reducible, then this seems true by induction. I'm...

Ohh, I think I finally get it! (after thinking about it for a loong while...) Infinity is hard for me to wrap my head around. Thanks a lot for your help.

Homework Statement Prove that the union of c sets of cardinality c has cardinality c. Homework Equations The Attempt at a Solution Well, I could look for a one-to-one and onto function... maybe mapping the union of c intervaks to the reals, or something? I know how to demonstrate...

Oh, okay. The sin(1/x) in the second derivative makes it not continuous. Thanks for your help.

Um, I understand that that would work, but I don't think I know how to take an antiderivative of that (or am I just being silly?) Are you suggesting I just write it as the integral of that?

I need to find an example of such a function. I know that x^2sin(1/x) is differentiable but not C^1, but I'm having trouble extending this to C^2.