Recent content by zeebo17

Hi, I have a question about integrating an numeric solution to a differential equation in Maple. I have solved a system of 3 odes: sol := dsolve({initial, syst}, func, numeric) where syst := diff(OmegaLambda(x), x) = ode1, diff(OmegaK(x), x) = ode2, diff(lnH(x), x) = ode3. This then gives me...

Oh! Great, thanks!

Homework Statement I need to solve \int_L \bar{z}-1 where L is the line from 1 to 1+2i. Homework Equations The Attempt at a Solution I know that I need to set z equal to the equation of the line and then integrate, but in this case I'm not sure how to express the equation of...

Hi, I was wondering if two sets are disjoint countably infinite sets why is their Cartesian product also countably infinite? Thanks!

Ok, great- Thanks! I think I can get the rest from there. The other thing I was wondering about was how to deal with that when A it is instead a countably infinite set. My book says that they would be equal in this case, but I'm not sure I see how.

The bar means the number of elements in that set.I'm trying to understand what the difference is between \overline{F(A \times A)} and \overline{F(A) \times F(A)} so I can determine which has the most elements or which is "bigger'."

I'm not sure, the book refers to F(A) as the power set.

I just started learning some basic measure theory. Could someone explain the difference between \overline{F(A \times A)} and \overline{F(A) \times F(A)} where A is a finite set. Also, how would this be different in A was an countably infinite set? Thanks!

I just started learning some basic measure theory. Could someone explain the difference between \overline{F(A \times A)} and \overline{F(A) \times F(A)} where A is a finite set. Also, how would this be different in A was an countably infinite set? Thanks!

What is 1/7 in base 2? How would you solve for this? Thanks!

Ok, Would this work: If h(x)> h(a) then h(x)>0 since h(x)>h(a)>0. If h(x)<h(a) then h(a)-h(x) > 0. Then because h is a continuous function there exists a \delta>0 such that |x-a|< \delta implies that |h(x)-h(a)|< \epsilon . In this case h(a)-h(x) > 0, so 0 < h(a)-h(x) < \epsilon...

Sorry, say we have a series f(x)= \Sigma n \cos(nx) e^{-n^2 x} and know that is converges uniformly on some interval [a, \infty) could we then conclude that it was continuous for all x in [a, \infty) ? I know there is a theorem that says that in order for there to be uniform...

Yes, that makes sense intuitively. I'm still unsure how to start writing a formal proof though.

If we know that some function f(x) converges uniformly on some interval does that imply that it is also continuous on the interval?

Homework Statement Let h: \Re \rightarrow \Re be a continuous function such that h(a)>0 for some a \in \Re. Prove that there exists a \delta >0 such that h(x)>0 provided that |x-a|< \delta . Homework Equations Continuity of h means that there exists and \epsilon >0 such that...