Recent content by Berrius

Thanx. But I think this approach is beyond the scope of my course. I was specifically told to look at the taylor expansion of ln(2). Is there a way to do it that way?

Homework Statement As part of a problem I have to show that lim_{n\to\infty}\sum_{i=\frac{n}{2}}^{n}\frac{1}{i}=ln(2) Homework Equations Taylor expansion of ln(2): \sum_{i=1}^{\infty}\frac{(-1)^{k+1}}{k} The Attempt at a Solution ln(2) can be written as: ln(2) =...

I have to prove that the cardinality of the set of infinite sequences of real numbers is equal to the cardinality of the set of real numbers. So: A := |\mathbb{R}^\mathbb{N}|=|\mathbb{R}| =: B My plan was to define 2 injective maps, 1 from A to B, and 1 from B to A. B <= A is trivial, just...

I know ofcourse ||v||=0 iff v=0, but why is this still true when i put a limit in front of it?

This is not really a homework question, but I've come across this while preparing for a test Homework Statement Let f:U \subseteq R^n -> R^m be a function which is differentiable at a \in U, and u \in R^n It is then stated that it is clear that: lim_{t \to 0}...

With homogeneous I just ment the differential equation without the constant part. But your approach won't work because u'(t)=u_1'(t)+u_2'(t)=-c(a+b)u_1(t)+cu_1^2(t)-c(a+b)u_2(t)+cab=-c(a+b)u(t)+cu_1^2(t)+cab Or am I seeing it wrong?

Homework Statement Find a solution for: u'(t)=c*u(t)^2-c*(a+b)*u(t)+c*a*b The Attempt at a Solution I've found the solution for the homogeneous equation: u_0(t)=(\frac{1}{a+b}+d*e^{c(a+b)t)})^{-1} Where c is a random constant. Now I've tried the solution u(t)=x(t)*u_0(t), when I fill...

Yes, but I'm writing a text non-mathematicians so I'm searching for for a very concrete example.

Hi there, Im looking for a theorem that relies on the axiom of choice, but is used in applied mathematics (economics, physics, biology, whatever). In other words a mathematical theory we use to say something about the real world. This is because I'm wondering if discarding the axiom of...

Homework Statement Given an infinite long (in the z-direction), with width 2b in the y-direction and no thickness in the x-direction. There is a current with density J in the z-direction. Calculate the magnetic field on the y-axis if |y| > b. Homework Equations Amperes law: ∫B*dS = μ0*I...

So if I say something like: 7x^2+2y^2 \leq 6 \Rightarrow y^2 \leq 3 \lt 4 \Rightarrow y \lt 2 and 7x^2+2y^2 \leq 6 \Rightarrow x^2 \leq \frac{6}{7} \lt 1 \Rightarrow x \lt 1 and z \leq x^2y+5y^3 \Rightarrow z \lt (2+5*8)=42 So choose M = 4+1+42^2 = 1769. And this M will do.

Homework Statement Show that D = { (x,y,z) \in \mathbb{R}^{3} | 7x^2+2y^2 \leq 6, x^3+y \leq z \leq x^2y+5y^3} is bounded. Homework Equations Definition of bounded:D \subseteq \mathbb{R}^{n} is called bounded if there exists a M > 0 such that D \subseteq \{x \in \mathbb{R}^{n} | ||x|| \leq...

X would be it's power set, and thus there would be a bijection between them. However I've proven there doesn't exist a bijection. In other words, X and it's power set have the same cardinality (if X exists), but I've proven the power set is bigger than X, so there is a contradiction and thus X...

Yes I've proven that there doesn't exist a surjection f: S \rightarrow \wp(S), but there exists an injection.

Homework Statement Prove a set which contains all of it's subsets doesn't exist. The Attempt at a Solution Suppose such a set P exists. P := {x | x \in \wp(x)}. P \in \wp(x), so P \in P. This seems like a paradox to me, so all I have to prove is that a set can't contain itself. But how...