Recent content by dane502

Thank you. Somehow I missed that.

Thank you for your answer. No, the half-open intervals has to be on the form of [a,b), so any union of those half-open intervals (that is not disjoint) will also have form [a,b).

Hi everybody! I have been asked to show that the Borel-algebra can be generated from the set of half-open intervals of the form [a , b) where a<b. I know that the set of open intervals of the form (a,b) where a<b generates the Borel-algebra and thought I would go about showing that the to...

I only have maple, and it is unable to evaluate the sum. Does anybody have another idea?

Try using separation of the variables.

If I may add another question to the above, are the two sets equal for ε→0?

That is a convincing argument, although I have a hard time visualizing the difference between the two sets, when ε→0.. With regards to the original topic, I have another question. We have shown that the series converges uniformly, which is all I needed to show, but i would also like to know to...

Got it! Thank you very much, LCKurtz. For my personal interest, would someone care to comment on whether or not the sets \mathbb{R}\backslash\ \left\{ 0 \right\} and \mathbb{R}\backslash\ \left] -\epsilon,\epsilon \right[ where \epsilon>0, are the same?

Homework Statement Prove that the series \sum_{n=0}^\infty e^{-n^2x^2} converges uniformly on the set \mathbb{R}\backslash\ \big] -\epsilon,\epsilon\big[ where \epsilon>0Homework Equations n/aThe Attempt at a Solution I have tried using Weierstrass M-test but I have not been able to find a...

Please note that I have chosen my pivots by Bland's rule

Homework Statement I am trying to solve the follwing linear program \max \qquad 4x_1+x_2+3x_3 \text{s.t }\qquad x_1+4x_2\qquad\,\leq1 \quad\quad\quad\quad\quad\quad3x_1-x_2+x_3\leq3 The Attempt at a Solution Using the simplex method and a tableau (negated objective function in the last...

Thanks for your fast response - Your right. The entry in column 3 row 1 should be a 0 and not a 1. Which makes \text{Rk}(\underline{\underline{A}}^n) = \text{Rk}(\underline{\underline{C}}^n) for all n\in\mathbb{N} . Would someone care to comment on whether or not the dimension of the...

First of all I would like to wish a happy new year to all of you, who have helped us understand college math and physics. I really appreciate it. Homework Statement Determine the dimension of the image of a linear transformations f^{\circ n}, where n\in\mathbb{N} and...

Okay, so if my proof consisted of proving, that n_1 < n_2 and then using the "induction" used in my previous post, it wouldn't complete the proof that n_k < n_(k+1) for all integers, k?

I am to prove something inductively. Can one substitute as follows? For the inductive part, assume that (*) n_k < n_(k+1) In order to show that this implies: (**) n_(k+1) < n_(k+2), Can one then simply make the substitution k+1 = s in (**), yielding n_(s) < n_(s+1)?