Closed Definition and 1000 Threads

How is the age of the universe measured? Is it by the distance light has traveled since the big bang? Does that imply a closed universe?

Homework Statement Create a closed form for: ƒn = 14ƒn − 1 − 32ƒn − 2 + 24ƒn − 3 Homework Equations Initial conditions: ƒ(0) = 2 ƒ(1) = 5 ƒ(2) = 11 The Attempt at a Solution Because it's 3rd order, it has me confused as how to start it. I was thinking something along the...

there is a function: F ( x, y, z) = 2ln (xz) + sin ( xyz) − y^2 = 0. the func is defined by the closed function z=f(x,y) and provides : f(1,0)=1 we define: g(t)=f(t,1-t^6) . where t is very close to 1. I have to find g'(1)Homework Equations I tried to to do like that: find F'x and F'z and did...

The rational (and also algebraic) elements of ℂ are closed under addition, multiplication, and rational exponentiation (the algebraic numbers, that is), but not under complex exponentiation. For instance, (-1)^i=e^{-\pi}, with is not rational, and in fact it is even transcendental. Is there any...

Homework Statement A particle moves in the central force field \overrightarrow{F}=-kr^{n}\hat{r} , where k is a constant, and r is the distance from the origin. For what values of n closed stable orbits are possible? Homework Equations The Attempt at a Solution I thought for...

Homework Statement 1. A piston cylinder arrangement ( A = 0.25 m^2, P1= 200 KPa, V1= 0.05 m^3. is loaded with a linear spring. in the current configuration the spring exerts no force on the piston head. if the atmospheric pressure is 101 KPa, what is the mass of the piston head. Heat is now...

Topology Proof: AcBcX, B closed --> A'cB' Homework Statement Prove: AcBcX, B closed --> A'cB' and where the prime denotes the set of limit points in that set X\B is the set difference Homework Equations Theorem: B is closed <--> For all b in X\B, there exists a neighborhood U...

Homework Statement A pipe resonates at successive frequencies of 540 Hz, 450 Hz, and 350Hz. Is this an open or a closed pipe? Homework Equations L = (nλ)/2 or L = ((2n-1)/4)λ v = fλThe Attempt at a Solution The difference between the first two frequencies (540 & 450) is 90Hz, and the...

Homework Statement Show by example that an infinite union of closed sets in \mathbb{C} need not be closed. The Attempt at a Solution In \mathbb{R} I know that an infinite union of the closed sets A_{n}=[1/n,1-1/n] is open. Not sure if it works in \mathbb{C} as well.

Homework Statement Find an infinite intersection of open sets in C that is closed. The Attempt at a Solution Consider the sets A_n = (-1/n,1/n). Since 0 in A_n for all n, 0 in \bigcap A_{n}. Here I'm a little stuck -- is the proof in R analogous to the proof in C, or do I need a...

This is always zero, right? What if you construct a closed surface which only encompasses one of the poles of a magnet? Surely there would then be a non-zero flux as the inside of the surface would constitute a source (or sink) of magnetic field lines. I'm new to electromagnetism, so any...

I've been researching this for quite a while and feel somewhat exasperated, so I thought I would ask more knowledgeable folk. I need to seal a closed system for low vacuum, and I need to do it on a budget. My problem is that most of the information I have found deals with much higher vacuums...

We wrap a light, flexible cable around a thin-walled, hollow cylinder with mass M and radius R. The cylinder is attached to the axle by spokes of a negligible moment of inertia.The cylinder rotates with negligible friction about a stationary horizontal axis. We tie the free end of the cable to a...

When considered as a subset of \mathbb{R}^2, \mathbb{Z} is a closed set. Proof. We will show, by definition, that \mathbb{Z} \subset \mathbb{R}^2 is closed. That is, we need to show that, if n is a limit point of \mathbb{Z}, then n \in \mathbb{Z}. I think this becomes vacuously true, since our...

Homework Statement Prove if $f$ is measurable on R and C is any closed set, f^{-1}(C) is measurable. Homework Equations Definition of measurability, closed sets etc. The Attempt at a Solution I've been trying for a while to get this proof, but I seem to just end up stuck at the...

\int_\alpha\frac{1}{z^2}dz I can't figure out how to integrate this over a closed circle which contains the origin on its interior. I'm assuming it is equal to 2πi; is there a way to apply Cauchy's Integral Theorem? If I set f(z)=1/z then that is not analytic on the interior, so I don't see...

Let I be an open interval and f : I → ℝ is a function. How do you define "f is continuous on I" ? would the following be sufficient? : f is continuous on the open interval I=(a,b) if \stackrel{lim}{x\rightarrow}c \frac{f(x)-f(c)}{x-c} exists \forall c\in (a, b) is this correct? Also, what...

A question about the simplest of things: Based on the physics of sound, how can you hear someone through a closed door? I'm quite confused because someone once told me its was because the sound passes through the door; since its causing the air molecules to vibrate, when this vibration hits...

Homework Statement Let {xn} be a sequence of real numbers. Let E denote the set of all numbers z that have the property that there exists a subsequence {xnk} convergent to z. Show that E is closed. Homework Equations A closed set must contain all of its accumulation points. Sets with no...

What is the difference between a closed Universe and an open Universe? Please explain in layman's terms and describe what type our Universe is.

This problem is from Mathematical methods for physicists by Arfken, problem 6.4.7. A function f(z) is analytic within a closed contour C (and continuous on C). If f(z) ≠ 0 within C and |f(z)|≤ M on C, show that |f(z)|≤ M for all points within C. The hint is to consider w(z) = 1/f(z). I have...

So I have to find an infinite union of closed sets that isn't closed. I've thought of something that might work: \bigcup[0,x] where 0\leq x<1. Then, \bigcup[0,x] = [0,1), right?

hi, I've got a problem which I cannot solve. The problem says that How long does it take to produce H2 in a closed beaker with volume 5l pressure 10Mpa and temp. 20 C with a current of 0.7A. First thing I did was to calculate the amount of H2 in that beaker. Assuming that it behaves ideally I...

Homework Statement If f:\mathbb{R}\to\mathbb{R} and g:\mathbb{R}\to\mathbb{R} are continuous functions show that: (a) the graph of f, \{(x,f(x)) : x\in\mathbb{R} \} is a closed subset of \mathbb{R}^2. (b) \{ (x,f(x),g(x)) : x\in \mathbb{R} \} is a closed subset of \mathbb{R}^3. The...

Suppose f:\mathbb{R}\to \mathbb{R} is a continuous function (standard metric). Show that its graph \{ (x,f(x)) : x \in \mathbb{R} \} is a closed subset of \mathbb{R}^2 (Euclidean metric). How to show this is closed?

Homework Statement Theorem: Given a metric space \left(X,d\right), the set of all limit points of a subset E\subset X, denoted E' is a closed set. I have an Analysis Exam tomorrow and have been studying for quite awhile and last week, my professor gave us a list of Theorems to know the proofs...

Homework Statement Two infinitely long current carrying wires run into the page as indicated. Consider a closed triangular path that runs from point 1 to point 2 to point 3 and back to point 1 as shown. Which of the following plots best shows B•dl as a function of position along the closed...

Homework Statement I should derive the Hubble law redshift from Maxwell equations in closed Universe. Homework Equations The metric of closed Universe is ds^2 = dt^2 - a^2(t)\left(d\chi^2 + \sin^2 \chi d\theta^2 + \sin^2 \chi \sin^2 \theta d\phi^2\right). The Hubble law redshift: \frac...

Homework Statement Show that the function f: J → ℝ is bounded if f is uniformly continuous on the bounded interval J. Homework Equations J is a bounded interval, so say J = (a,b) f is uniformly continuous on J, so \forall \epsilon > 0 there exists a \delta > 0 such that for s,t \in J...

Hi, I am measuring pressure at the bottom of a fuel tank and temp variations are giving me a tough time. I wish to clear my head so here goes my reasoning as temp increases - Tank Volume increases causing - height of fuel to decrease, pressure at the bottom of tank to decrease - Fuel...

This was a problem on a recent graduate level introductory analysis midterm. The entire class completely bombed (class average was 18%), so we have to rewrite the exam as homework. So with those considerations, i don't want any explicit help, but feedback on the other hand would be great. I'm...

Hi! I have used the physics forum a lot of times to deal with several tasks that I had and now its the time to introduce my own query! So please bear with me :-) Homework Statement Equip the set C^1_{[0,1]} with the inner product: \left\langle f,g \right\rangle= \int_{0}^{1}...

Originally posted on sciforumsDOTcom by me (DRZion): So I came up with a scenario which is simple enough for anyone to understand. You take a fluid which is liquid at room temperature, but freezes to a become a solid denser than the liquid. This is done to any amount of liquid at the...

Homework Statement The figure below shows a plot of temperature T versus entropy S for the closed cycle of a particular heat engine (not necessarily an ideal gas) which consists of 3 processes and which operates between two heater reservoirs, a hot reservoir with temperature T1 and a cold...

Homework Statement Determine whether the following statements are true or false a) Every pairwise disjoint family of open subsets of ℝ is countable. b) Every pairwise disjoint family of closed subsets of ℝ is countable. Homework Equations part (a) is true. we can find 1-1...

Homework Statement It is number three on the following page. http://people.math.carleton.ca/~mezo/A3math1102-11.pdfHomework Equations No idea. The Attempt at a Solution I have no idea how to incorporate the kj. Best I could reason through this is supposing: b1 ∈ N(A) , c1 ∈ N(A) Ab1 +...

So the voltage drops across closed circuits I get that is P = V^2/R to get the power and then you will use P=I^2/R to get the current running through the circuit and in the case the current flowing through the closed circuit is equal in every resistor and so is the voltage drop. The part that I...

While trying to get my head around Gravitational Potential Energy I devised the following simple system: Point Mass A of 1kg is 1000m away from Point Mass B of 100kg within an empty universe. The gravitational force exerted by A on B is G*10^-16; by B on A is G*10^-4. At time=0 these two...

Homework Statement Let M, N be two metric spaces. For f: M --> N, define the function on M, graph(f) = {(x,f(x)) \inMxN: x\inM} show f continuous => graph(f) is closed in MxN Homework Equations The Attempt at a Solution I can't figure out what method to use. I have...

Homework Statement Show that every compact set must be closed. I am looking for a simple proof. This is supposed to be Intro Analysis proof. Relevant equations Any compact set must be bounded. The Attempt at a Solution Suppose A is not closed, so let a be an accumulation...

Because of the kinetic energy and frames of reference thread: https://www.physicsforums.com/showthread.php?t=534883 I was wondering how to show that a change from potential to kinetic energy in a closed system is independent of the (inertial) frame of reference. I think the math below...

Homework Statement Let M be a metric space, A a subset of M, x a point in M. Define the metric of x to A by d(x,A) = inf d(x,y), y in A For \epsilon>0, define the sets D(A,\epsilon) = {x in M : d(x,A)<\epsilon} N(A,\epsilon) = {x in M: d(x,A)\leq\epsilon} Show that A is...

(a) Find the surface area, S, as a function of r. S = 2*pi*r^2 + 2*pi*r*h I know how the 2pi(r)^2 is found, but where does the 2*pi*r*h come from? (b) What happens to the value of S as r goes to infinity? S also goes to infinity. As r increases, S increases. (c) Sketch a graph of...

Hey everyone, This is a review of some stuff I learned in high school, but I haven't actually done anything calculus related in about 2 years, and to be honest it looks foreign to me, if someone could help jog the old noodle it would help tremendously. The first question is as follows...

Homework Statement Prove that {(a1, a2) ∈ R2 : 0 ≤ a1 ≤ 2, 0 ≤ a2 ≤ 4} is a closed set in the Euclidean metric. Homework Equations Not sure The Attempt at a Solution How do I approach this problem? Do I prove there is a closed ball in my set? Or, do I prove there is an open ball...

Homework Statement Q = rational numbers My professor proved that it is closed under addition yesterday. I kinda understood a bit... How the heck does it work for when n_1 or n_2 = 0?

X = [0, 1] \bigcup (2,3) is phase space. Show that (2, 3) open and closed set of X . the question is like that but I think it is false because it is not close, right?

This is the question: Let A be an open set and B a closed set. If B ⊂ A, prove that A \ B is open. If A ⊂ B, prove that B \ A is closed. Right before this we have a theorem stated as below: In R^d, (a) the union of an arbitrary collection of open sets is open; (b) the intersection of any...

Suppose a vector X of length n, where each component of X is normally distributed with mean 0 and variance 1, and independent of the other components. I want to know the probability that at least one of X_1>2, X_2>2.5, X_3>1.9, etc. happens (inclusive), i.e. the probability that the vector's...

Hi everyone, I was studying eletrodynamics and I've found the the following question In ideal circuit of the figure, initially opened, the capacitor of capacitance CX is initially loaded and stores a eletric potencial energy E. The capacitor of capacitance CY = 2CX is initially...