Recent content by MrGandalf

Yes, I agree, and your reasoning seems a bit nicer. However, I'm not free to choose the intervals as I please, since I have derived them from the expectation of an elementary approximation of a Brownian motion. In addition this is just a small sub problem I ran into during a 7 page proof in...

Hmmm, not sure. But do we have to worry about that when we have showed that it has an upper bound of 0? (Which also works for the absolute value I think, so it can't be negative). Also, the "result" I reached over isn't really very solid, as it didn't work when I tried inserting x^2, but I...

I am summing the square of of many small intervals (s_{j+1} - s_j) := \Delta s_j. I take the biggest partition and multiply ever term in the sum with that instead, and that is where I get the inequality: (s_{j+1} - s_j)^2 = (\Delta s_j)^2 \leq \max_k(\Delta s_k)\Delta s_j When I pass...

Hi, stevenb, thanks for answering. But I think I got it. I will edit this post with my full answer, so you don't waste your precious time verifying this for me. Using the rule of a squared sum, which is what I started with: \left(\sum_i a_i\right)^2 = \sum_i a^2 + 2\sum_{i<j}a_ia_j In my...

Homework Statement This isn't a problem, it is just a small verification I need in a much larger proof. Over the interval [0,t] we define a partition: 0 = s_0 < s_1 < \ldots < s_{n-1} < s_n = t I have: \sum_{i<j}(s_{j+1} - s_j)(s_{i+1} - s_i) Homework Equations What I need...

Thanks. I was just really unsure there for a moment, but I think I see it now. Thanks for clearing that up for me. PS Sorry about the typo in the thread title.

Hiya. :) While doing an assignment I ran into this little problem. We are working in the set of natural numbers \mathbb{N}. If i collect each natural number in a set S_1 = \{1\}, S_2 = \{2\},\ldots, S_n = \{n\},\ldots What happens when I take the countable union of all these? S =...

Ah, of course! Thanks for explaining this to me.

Thanks for all your answers. I am still not sure how to show mathematically how +/- i will maximize the function. I tried doing a geometrical approach with drawing a circle with radius 3 and center in -1, but I can't see how it becomes obvious where it is maximized... I also failed to see...

Hi. I need someone to look at my attempt at a solution, and guide me towards the correct way to solving this. Thanks. Homework Statement Determine the maximum value of |3z^2 - 1| in the closed disk |z| \leq 1 in the complex plane. For what values of z does the maximum occur? The attempt...

Thank you! I will charge the proof with newfound courage and motivation. :)

I have a sneaky suspicion that this is a fairly simple task, but I just can't seem to break through this particular proof. Homework Statement The (Lebesgue) outer measure of any set A\subseteq\mathbb{R} is: m^*(A) = inf Z_A where Z_A = \bigg\{\sum_{n=1}^\infty...

Yes! Of course! How could I miss that? :) Thank you for helping me!

I was stumped by this differential equation. The function x = x(t). x^{\tiny\prime\prime} + \frac{1}{t}x^{\tiny\prime} = 0. You have the initial values x(a) = 0 and x(1) = 1. What I did was to introduce a new function u = x', so I ended up with the first order homogenous DE: u^{\tiny\prime} +...

Homework Statement We have f(z) = \frac{1}{z^2 - 2z - 3} For this function, we want to find the Laurent Series around z=0, that converges when z=2 and we want to find the area of convergence. Homework Equations \frac{1}{z-3} = -\frac{1}{3}\bigg( \frac{1}{1 - \frac{z}{3}}\bigg) =...