Closed Definition and 1000 Threads

ln(-1)/i=pi this equation does not use limits or integrals, as you can see, but it does involve imaginary numbers. Does this make it an open expression, or does the fact that it uses i not matter?

So here are my steps, which for some reason I feel are very wrong: Well in closed form would be [n(n+1)]/2 so 2k would be 2*[n(n+1)]/2 For 1.7^k, I used a different form, which I don't have the formula for in front of me, but the final result for that part is [1.7^(n+1) - 1] /[1.7 - 1] So...

Definition: A semigroup is a pair (R,op) where R is a set an op is a binary operation that is closed and associative. A commutative semigroup is a semigroup where op satisfies for all a,b in R, op(a,b) = op(b,a). A monoid is a semigroup where with an identity,e, for op, satisfying for all r in...

Homework Statement Prove or disprove the following statement: The closure of a set S is closed. Homework Equations Definition of closure: set T is the closure of set S means that T is the union of S and the set of limit points of S. Definition of a closed set: set S is...

Is it correct to make the following statement? If a point x in E is not a limit point of E, then any neighborhood V of x will--at most--contain finitely many points of E. Thus, its possible for V to contain only one point, namely, x. Thanks, M

Homework Statement 5 A closed wire loop in the form of a square of side 4.0 cm is mounted with its plane horizontal. The loop has a resistance of 2.0 x 10-3Ω, and negligible self-inductance. The loop is situated in a magnetic field of 0.70 T, directed vertically downwards. When the field is...

Am I missing something and doing this all wrong? Experiment and data: The level of water in the glass tube was adjusted by raising the supply tank until the sound from the tuning fork was at its loudest. This level corresponds to first resonance position and it was recorded. The...

Homework Statement Let X be an ordered set where every closed interval is compact. Prove that X has the least upper bound property. Homework Equations X having the least upper bound property means that every nonempty subset that is bounded from above has a least upper bound, in other...

I am modelling a free damped simple pendulum and was wondering if anyone could refer me to a paper or perhaps provide me with an expression describing the motion of the pendlum with large initial amplitude. I have solved the equations numerically but am implementing an optimization routine and...

I am modelling a free damped simple pendulum and was wondering if anyone could refer me to a paper or perhaps provide me with an expression describing the motion of the pendlum with large initial amplitude. I have solved the equations numerically but am implementing an optimization routine and...

Has anyone ever seen the treatment of a closed classical string loop. Like if you had a loop of string on the space shuttle and subject it to accoustic driving or initial impulses. I post this here in beyond the standard model because no one in the classical physics section seems to have heard...

Has anyone seen a treatment of how to use the wave equation to describe a closed loop of string. I am talking ordinary strings here not the fancy string theory kind.

Hi All, So all closed interval [a,b] is compact (see Theorem 2.2.1 in Real Analysis and Probability by RM Dudley) Now, Let's say I have [0,10] as my closed interval. Let My Open Cover be (0, 5) (5, 7.5) (7.5, 8.75) (8.75, 9.375) ... Essentially, The length of each open...

Homework Statement proove is either true of false let A be a set of integer closed under subtraction. if x and y are element of A, then x-ny is in A for any n in Z. Homework Equations n/a The Attempt at a Solution is there any proof, without induction? i suspect its true because any...

I am working on an incubator/shaker for laboratory use. I am trying to work out a temperature failure and repair it, but that is besides the point here. I was looking through the user manual to try to get some clues about the failure and I came across this: "Depending on various conditions...

Dear all, Is there a method to find the maximum and minimum dimension of an irregular closed loop? This is a problem when we want to define the full-width - half maximum of a image. The level contour of this image at its half maximum can be an irregular closed loop. Any reference or...

Consider a vertical pipe partially filled with liquid. The pipe is open at the lower end and closed at the top. See the attached picture. Will the liquid fall out or not? In a small diameter pipe a stable meniscus will form due to surface tension and prevent the water from falling out. In a...

Me again. Problem. Let X be a topological space, and Y a T2-space (i.e. a Haussdorf topological space). Let f : X --> Y be a continuous function. One needs to show that the graph of , i.e. the set G = {(x, f(x)) : x is in X} is closed in X x Y. Attempt of proof. To show what we need to show...

"Open" and "closed" in the geometrical sense vs the thermodynamic sense Perhaps this is a silly question, but what is the relationship between the words "open" and "closed" in the geometrical sense (open, flat, closed universes) and in the thermodynamic sense (open and closed systems) in the...

In case you have never heard of the elephant toothpaste experiment, take a look at this: http://www.using-hydrogen-peroxide.com/elephant-toothpaste.html" I was just wondering, if you put the chemicals together in an air tight container, would the air pressure increase?

im trying top find the flow rate of water from a closed pipe. one thing that i think i can work with is a hose. there is a hose branching of the main flow pipe, which can be used to clean floor etc. im thinking that i can not open the hose and thus measure the stagnatiob pressure at the...

So, I'm going through a proposition, which states that if (X, d) is a metric space, then any set {x}, where x e X, is a closed subset of X. First of all, could we do this proof to assume the contrary? Since then obviously for the point x from {x} there doesn't exist any real number r > 0 such...

First of all I just want to rant why is the Latex preview feature such a complete failure in Firefox? Actually it is really bad and buggy in IE too... So I am reading into Foundations of geometry by Abraham and Marsden and there is a basic topology proof that's giving me some trouble. They...

Homework Statement Giving 2 closed curves in 3-dimension space C1 and C2, prove that:\oint _{C1} \oint _{C2}\frac{(\vec{dl_2}.\hat{r_{12}})\vec{dl_1}}{r^2_{12}}=0 Where: _ \vec{dl_1} and \vec{dl_2} are the vector elements of the curves C1 and C2 respectively. _ r_{12} is the distance between...

Homework Statement An LED is connected as shown (see attached) When switch S is closed: A. the p-n junction is reverse biased and free charge carriers are produced which may recombine to give quanta of radiation. B. the p-n junction is forward biased and positive and negative charge...

Why does work done by a conservative force = 0 in a closed path? I know this sounds foolish :rolleyes: but how can some forces have such a property? Can anybody give a satisfactory physical explanation?:confused:

Homework Statement A long bar magnet is bent into the form of a closed ring. If the intensity of magnetisation is M, and ignoring any end effects due to the join, find the magnetic field H and the induction B: (a) Inside the material of the magnet (b) just outside Homework Equations...

Homework Statement Find the closed form value for n SIGMA e^(i/n) i= 0 Homework Equations ? The Attempt at a Solution summation expands to 1 + e^(1/n) + e^(2/n) - - - - - e^1 To be honest i have no clue how to go about these kinds of problems so a general help would...

Homework Statement In Rosenlicht's Intro to Analysis, there is a proposition (p. 52). A Cauchy sequence of points in a metric space is bounded. Proof: For if the sequence is P1, P2, P3, ... and ε is any positive number and N an integer such tat d(Pn, Pm) < ε if n, m > N, then for any...

Homework Statement I am using Rosenlicht's Intro to Analysis to self-study. 1.) I learn that the complements of an open ball is a closed ball. And... 2.) Some subsets of metric space are neither open nor closed. Homework Equations Is something amiss here? I do not understand how...

First post, please excuse my ignorance. If the Universe is closed, then at the end of the expansion, micro gravity eventually pulls all objects together. Black holes absorb more and more stars and whole galaxies and eventually each other until there is just one black hole and no matter left...

Homework Statement A = \left\{(x,y): 0\leq xy \leq 1\right\}, A \in R^{2} I'm trying to determine if this set is bounded and/or closed. Homework Equations if X = (x,y) euclidean metric: ||X|| = \sqrt{x^{2}+y^{2}} The Attempt at a Solution I know a bounded set =>...

Homework Statement on the complex line, with the usual metric, I need to determine if this is a closed set. A = \left\{\left|\frac{1}{z^{2}+1} \right|: |z| = 1 ; z\neq \pm i\right \} Homework Equations The Attempt at a Solution A closed set implies that the set of all limit points belongs...

Homework Statement Let (X,\tau_X) and (Y,\tau_Y) be topological spaces, and let f : X \to Y be continuous. Let Y be Hausdorff, and prove that the graph of f i.e. \graph(f) := \{ (x,f(x)) | x \in X \} is a closed subset of X \times Y. Homework Equations The Attempt at a Solution...

Homework Statement Let (X_a, \tau_a), a \in A be topological spaces, and let \displaystyle X = \prod_{a \in A} X_a. Homework Equations 1. Prove that the projection maps p_a : X \to X_a are open maps. 2. Let S_a \subseteq X_a and let \displaystyle S = \prod_{a \in A} S_a \subseteq...

Homework Statement Let l∞ be the space of bounded sequences of real numbers, endowed with the norm ∥x∥∞ = supn∈N |xn | , where x = (xn )n∈N . Prove that the closed unit ball of l∞ , B(0, 1) = {x ∈ l∞ ; ∥x∥∞ ≤ 1} , is not compact. Homework Equations The Attempt at a Solution I'm...

Apostol page 386, problem 5 Homework Statement Given f,g continuously differentiable on open connected S in the plane, show \oint_C{f\nabla g\cdot d\alpha}=-\oint_C{g\nabla f\cdot d\alpha} for any piecewise Jordan curve C. Homework Equations 1. Green's Theorem 2. \frac{\partial...

If (X,\tau) is either a T_1 space or Hausdorff space then for any x \in X the singleton set \{ x \} is closed. Why is this the case? I can't see the reason from the definitions of the spaces. Definition: Let (X,\tau) be a topological space and let x,y \in X be any two distinct points, if...

Homework Statement A projecticle launcher is shown in the attachment. A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a...

Homework Statement An organ pipe has two successive harmonics with frequencies 1760 Hz and 2160 Hz. Is this an open or stopped pipe? Which two harmonics are these? What is the length of the pipe? Homework Equations L=v/2f The Attempt at a Solution I'm really just having trouble...

Homework Statement a) Let V be a normed vector space. Then show that (by the triangle inequality) the function f(x)=||x|| is a Lipschitz function from V into [0,∞). In particular, f is uniformly continuous on V. b) Show that a closed subset F of contains an element of minimal norm, that...

Homework Statement I've just found what I think is the Green's function for a source between two ideal conducting planes at x = 0 and x = l:Homework Equations G(x,x') = \Sigma \frac{icos(\pi n x/l)}{(\pi n /l)} The Attempt at a Solution The question then wants me to put...

I understand that magnetic flux through a closed surface is zero, but what is the exact definition of a closed surface? The textbook I'm using is rather vague with this definition and I want to make sure I have the definition nailed down for the exam in case my professor tries anything tricky.

So confused about standing waves in a closed pipe, which is open at one end and closed at the other. The closed end has a node while the open end has an antinode. To figure the wavelength, i use the formula: Lambda = 4L/n where n is the number of harmonic and can only be odd integers...

I'm reading Riley's "Mathematical Methods for Physics and Engineering" and I came across this expression about vector spaces: "A set of objects (vectors) a, b, c, ... is said to form a linear vector space V if the set is closed under commutative and associative addition (...)" What I don't...

We know that a linear operator T:X\rightarrowY between two Banach Spaces X and Y is an open mapping if T is surjective. Here open mapping means that T sends open subsets of X to open subsets of Y. Prove that if T is an open mapping between two Banach Spaces then it is not necessarily a closed...

[b]1. the lowest note on an organ is 16.4 Hz. What is the shortest open organ pipe that will resonate at this frequnecy? What would be the pitch if the same organ pipe were closed? [b]3. is the answer 32.8 meters and 65.6 meters?

I think cos(x) is closed function in R. But I heard that cos(x) is not closed function in R. What do I choose closed set A in R, cos(A) is not closed in R? Help...

how can i calculate density of a liquid pumped in a closed circuit and i don't know the nature of it ?

Homework Statement Let γ be a closed orbit of the flow φ on the manifold M and suppose there exists T>0 and X0 є γ such that φT(X0) = X0. Prove that φT(X) = X for every X0 є γ. Furthermore locate two closed orbits γ1 and γ2 and positive periods T1 and T2 for the flow of r ̇=r(r-1)(r-2); θ...