Continuous Definition and 1000 Threads

Homework Statement Homework Equations Continuity @ v0 The Attempt at a Solution Using the epsilon delta definition of continuity: If we choose epsilon such that epsilon < a, then |f(v) - f(v0)| < a. So f(v) is in the interval (f(v0) - a, f(v0) + a). Only half of this interval is what I want...

Hi there! I need to calculate the Fourier transform of a continuous function in C++. To do this I need to use the Dft, but what is the relation between the Dft and the continuous Fourier transform? I mean, how can I get the continuous Fourier transform from the Dft?

Homework Statement So, given a metric d : X x X --> R, prove that d is continuous.The Attempt at a Solution Let (x, y) be a point in X x X, V = <a, b> a neighborhood of d(x, y). One needs to find a neighborhood of U of (x, y) such that d(U) is contained in V. U is of the form U1 x U2, where...

Homework Statement Suppose X ~ uniform (0,1) and the conditional distribution of Y given X = x is binomial (n, p=x), i.e. P(Y=y|X=x) = nCy x^{y} (1-x)^{n-y} for y = 0, 1,..., n. Homework Equations FInd E(y) and the distribution of Y.The Attempt at a Solution f(x) = \frac{1}{b-a} = \frac{1}{1-0}...

Homework Statement Let S denote a unit circle centered at origin in xy plane, and f is a continuous function that sends S to R (no need to be 1 to 1 or onto). show that there's (x, y) such that f(x, y) = f(-x, -y) Homework Equations have a feeling it has something to do with theorems...

Homework Statement Given f : [-\sqrt{\pi}, \sqrt{\pi} ] \rightarrow [-1, 1] f(x) = sin(x^{2}) a) Show that f is continuous for all a \in [-\sqrt{\pi}, \sqrt{\pi} ] b) Find a \delta so that |x - y| \leq \delta implies that |f(x) - f(y)| \leq 0.1 for...

Homework Statement Let f : A --> Y be a continuous function, where A is a subset of X and Y is Haussdorf. Show that, if f can be extended to a continuous function g : Cl(A) --> Y, then g is uniquely determined by f. The Attempt at a Solution I think I can solve this on my own, but I...

Has it been considered to instead of quantizing gravity, and incorporating gravity into the quantum theory, but rather incorporating the other three forces into relativity?

Why is the traverse loading strength of continuous fibre reinforced composites weaker compared to the longitudinal strength? I sort of arrived at the conclusion, that since the composite is in an isostress state and due to the fibre having a very low tensile strength in the transverse...

Hi, In ch22, Srednicki considers the path integral Z(J)=\int D\phi \exp{i[S+\int d^4y J_a\phi_a]} He says the value of Z(J) is unchanged if we make the change of var \phi_a(x)\rightarrow\phi_a(x)+\delta\phi_a(x), with \phi_a(x) an arbitrary infinitesimal shift that leaves the mesure...

Homework Statement Let F be a function defined on a open set E where E \in V. F is said to be continuous at each point x \in V. Which according to my textbook at hand can be written as F \in \mathcal{C}(E) But the expression F \in \mathcal{C}^{1}(E) is that equal to saying that F have...

Homework Statement Find the values of a and b that make f continuous everywhere. (Enter your answers as fractions.) Homework Equations The Attempt at a Solution lim x->2 (x2-4)/(x-2) = 0 lim x->2 4a - 2b +5 lim x->3 9a - 3b +5 lim x->3 12 - a + b 4a - 2b + 5 = 0 4a...

Dear all, in basic QM books the position and momentum operators (continuous eigenvectors) are introduce by means of the dirac delta and some analogies are made with the infinite dimensional, but discrete case in order to provide some intuition for the integral formulas presented. My knowledge...

Homework Statement Let f:A\subset{\mathbb{R}}^{n}\mapsto \mathbb{R} be a linear function continuous a \vec{0} . To prove that f is continuous everywhere. Homework Equations If f is continuous at zero, then \forall \epsilon>0 \exists\delta>0 such that if \|\vec{x}\|<\delta then...

1. The accountants at HR office of the Sirius Cybernetics Corporation have determined that the company would need additional $10 billion in its pension fund account over and above the current projected amount at the end of year 2030. (a) Assuming the fund's balance will be growing, compounds...

Ive got a beam that I can't seem to calculate the loading of. Let's say beam ABC supports are at A & B, BC is a cantilever. There is no wall on AB, but there is a wall on BC. Now I have tried breaking it up into separate parts, but does not look right. I was taught the method of triangles and...

Is the space of all absolutely continuous functions complete? I've never learned about absolutely continuous functions, and so I'm unsure of their properties when working with them. I'm fairly certain it is, but would like some verification. Or a link to something on them besides the...

I've been looking over quantum gravity threads here for a year or so. One thing keeps puzzling me. It appears to me that difficulty coming up with a viable quantum gravity theory is melding the continuous nature of the general relativity equations with the discrete (i.e. quantized) nature of...

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How can the function f: ℝ² → ℝ : (x,y) |--> {{x^3-y^3}\over{x-y}} if x ≠ y be defined on the line y=x so that we get a continuous function?Is this correct?: If x=y --> f=0

How can the function f: ℝ² → ℝ : (x,y) |--> {{x^2+y^2-(x^3y^3)}\over{x^2+y^2}} if (x,y) ≠ (0,0) be defined in the origin so that we get a continuous function?When I take 'x=y' (so (y,y)) and 'y=x' (so (x,x)) I get: {{2-y^4}\over{2}} and {{2-x^4}\over{2}} So for the first one I get '1'...

The definitions of a harmonic function u are: It has continuous 1st and 2nd derivatives and it satisfies \nabla^2 u = 0. Is the second derivative equal zero consider continuous? Example: u=x^2+y^2 ,\; \hbox{ 1st derivative }=u_x + u_y = 2x+2y,\; \hbox{ 2nd derivative }=u_{xx} + u_{yy} +...

Homework Statement Suppose that f is continuous on (0,1) and that int[0,x] f = int[x,1] f for all x in [0,1]. Prove that f(x)=0 for all x in [0,1]. Homework Equations We know that since f is continuous on (0,1), F(x) = int[0,x] f and F'(x) = f(x) for x in (0,1). The Attempt...

Homework Statement A continuous random variable ,X represents the period, of a telephone call in the office. The cdf of x is given by F(x)= x^2/8 for 0<=x<=2 =1-4/x^3 for x>2 Find pdf , mean and variance. Homework Equations The Attempt at a Solution pdf: f(x) = 1/4...

I'm struggling to understand continuous functions as subspaces of each other. I use ⊆ to mean subspace below, is this the correct notation? I also tried to write some symbols in superscript but couldn't manage. Anyway I know that; Pn ⊆ C∞(-∞,∞) ⊆ Cm(-∞,∞) ⊆ C1(-∞,∞) ⊆ C(-∞,∞) ⊆ F(-∞,∞) I...

We know that dim(C[a,b]) is infinte. Indeed it cannot be finite since it contains the set of all polynomials. Is the dimension of a Hamel basis for it countable or uncountable? I guess if we put a norm on it to make a Banach space, we could use Baire's to imply uncountable. I am however...

I'd like to show that functions like x^a with a > 0 satisfy the Holder condition on an interval like [0, 1]. That is to say that for any x and y in that interval, then for example, |x^{\frac{1}{2}} - y^{\frac{1}{2}}| \leq C|x-y|^k for some constants C and k. What is the trick to proving...

Homework Statement Show x^2 is continuous, on all reals, using a delta/epsilon argument. Let E>0. I want to find a D s.t. whenever d(x,y)<D d(f(x),f(y))<E. WLOG let x>y |x^2-y^2|=x^2-y^2=(x-y)(x+y)<D(x+y) I am trying to bound x+y, but can't figure out how.

Homework Statement Let f(x) = x sgn(sin(1/x)) if x != 0 f(x) = 0 if x = 0 on the interval I=[-1,1] Now I 'm asked to show that f(x) is not piecewise continuous on I and later, I must show that f is integrable on I. The Attempt at a Solution I am completely lost here and...

Homework Statement Suppose f is a continuous function on [0,2] with f(0) = f(2). Show that there is an x in [0,1] where f(x) = f(x+1). Homework Equations By the Intermediate Value Theorem, we know that any values between sup{f(x)} and inf {f(x)} over x in [0,2] will be repeated...

can anybody please help me in solving the following question: consider the function on [0,1] f(x)=1/q if x=p/q, p&q are non zero & p,q are positive integers, p/q is in simplest form...

What determines whether an operator has discrete or continuous eigenvalues? Energy and momentum sometimes have discrete eigenvalues, sometimes continuous. Position is always continuous (isnt it?) Spin is always discrete (isn't it?) Why?

Hello. Are there any chemical reactions of the Briggs-Rauscher variety that will continue to oscillate indefinitely with continued agitation? B-R fades out after a few minutes of agitation, and I am curious as to whether there are oscillating reactions that will continue to oscillate as long as...

Homework Statement If H:I\rightarrowI is a monotone and continuous function, prove that H is a homeomorphism if either a) H(0) = 0 and H(1) = 1 or b) H(0) = 1 and H(1) = 0. Homework Equations The Attempt at a Solution So if I can prove H is a homeomorphism for a), b)...

My textbook describes how some functions are not well approximated by tangent planes at a particular point. For example f(x)= xy / (x^2 + y^2) for x /= 0 0 for x = 0 at (0,0) the partial derivatives exist and are zero but they are not continuous at...

I am reading Schutz's "Geometrical methods of mathematical physics". He writes: "A map f:M->N is continuous at x in M if any open set of N containing f(x) contains the image of an open set of M." However, it seems to me that a more appropriate definition would be "... contains the image of a...

Let F and y both be continuous for simplicity. Knowing that: \int_0^x F'(t)y^2(t) dt = F(x) \quad \forall x \geq 0 can you say that the function y is bounded? Why? I know that \int_0^x F'(t) dt = F(x) but I can't find a suitable inequality to prove rigorously that y is bounded.

If dim[FONT="Times New Roman"]M=m<p, show that every map(maybe continuous) [FONT="Times New Roman"]Mm -> [FONT="Times New Roman"]Sp is homotopic to a constant. This is the problem 5 in chap8. of 'topology from the differentiable viewpoint(Milnor)'. I proved it when the map is not...

part 2 The Electric Field of a Continuous Distribution of Charge Homework Statement find the electric potential at point p Homework Equations v=Kq/r...v=Er. The Attempt at a Solution using this pic above and dQ=(Q/L)(dX) v=(K)(dQ)/(L-(X_i)+d) then sub dq=dX(Q/L) we get...

There are no Bayesian Networks for continuous random variables, as far as I know. And the Netica Bayesian Network software discretize continuous random variables to build bayesian models. Are there any reasons for this? Has anyone proposed continuous random variable bayesian networks?

Hi I'm new to calculus and I'm teaching myself so please be kind to me :) How do you prove that f(x) = x is continuous at all points? I know a little bit about deltas and epsilons. I know that for a positive epsilon it is possible to get a delta such that |(fx) - L| < epsilon for all x...

Let (X; T ) be a topological space. Given the set Y and the function f : X \rightarrow Y , define U := {H\inY \mid f^{-1}(H)\in T} Show that U is the finest topology on Y with respect to which f is continuous. Homework Equations The Attempt at a Solution I was wondering is...

Homework Statement Define f(x)=sin(x)sin(1/x) if x does not =0, and 0 when x=0. Have to prove that f(x) is continuous at 0. Homework Equations We can use the definition of continuity to prove this, I believe. The Attempt at a Solution I know from previous homework...

Homework Statement I have to make a Buck-Boost converter for my Design PE class but the problem is even though i have read about them i seriously don't know where to start. I have to make calculations and choose a mosfet, load, capacitor and an inductor but i don't know how. Homework...

f(x,y) = x + y is the joint probability density function for continuous random variables X and Y. The support of this function is {0 < x < 1, 0 < y < 1}, which means it takes positive values over this region and zero elsewhere. g(x) = x + (1/2) is the probability density function of X...

So, I'm taking an EE class and my teacher is terribly handwavy. She couldn't really explain this to me (not homework, lecture). I detect a fundamental problem in the math, coming from a science background, but it could just be my ignorance: Here's her lecture: physical setup: a...

i'm having a difficult time trying to grasp what absolute continuity means, i understand uniform continuity. i can't seem to distinguish between the them. to me it seems that if f on some inteval [a,b] is uniformly continuous then it would be absolutely continuous ? is there a visual way...

Homework Statement Let f be a continuous function lR (all real numbers) --> lR such that f(x+y) = f(x) + f (y) for x, y in lR. prove that f(n) = n*f(1) for all n in lN (all natural numbers)Homework Equations f is continuous also note and prove that f(0) = 0 The Attempt at a Solution Edit...

Hi: Just curious: a continuous function f:X-->Y ; X,Y topological spaces, can fail to be an embedding because it is not 1-1, or, if f is 1-1 , f can fail to be an embedding because, for U open in X f(U) is not open in f(X). Can anyone think of a "reasonable" example of the...

Z = X + Y Where X and Y are continuous random variables defined on [0,1] with a continuous uniform distribution. I know we define the density of Z, fz as the convolution of fx and fy but I have no idea why to evaluate the convolution integral, we consider the intervals [0,z] and [1,z-1]...