Continuous Definition and 1000 Threads

Problem: Assume that f: [0,infinity) -> R is continuous at every point of its domain. Show that if there exists a b>0 so that f is uniformly continuous on the set [b,infinity) then f is uniformly continuous on [0,infinity). I don't really know where to start with this one, any help would...

Homework Statement Using the epsilon-delta definition, prove that the function f:R^{2} \rightarrow R by f(x,y) = xy/((x^{2}) + (y^{2})), and f(0,0) = 0 is not continuous. The Attempt at a Solution I just really have no clue how to set up a delta-epsilon proof for functions that involve...

Homework Statement (X,d) a compact metric space, f:X->X cts fn, with d(f(x),f(y)) >= d(x,y) for all x, y in X Prove that f is a surjection.The Attempt at a Solution Let K be the set of points that are not in f(X). It is a union of open balls because X is closed and hence so is f(X). Choose...

HI, A question which arises to me is about magnetic fields of a wire or a permanent magnet, Are they continuous? or are discontinuous like what we draw them when We want to show them in a paper? If they are continuous then why we see discontinuous lines when we make a test by iron's...

Not sure where to put this, but if it's wrong, sorry... I just looked at the Nieto, Anderson paper on arXiv: arXiv:0907.3418 "Earth Flyby Anomalies" Funnily enough, it's about anomalies in the velocity of probes doing Earth flybys! This has hit the scientific news (New Scientist this...

Homework Statement Consider a function f : R--> R, and assume that there is a c is in (0, 1) so that |f(x) - f(y)|<= c|x -y| for all x, y in R. (a) Show that f is continuous on R. (b) Given a point y1 in R define a sequence by yn+1 = f(yn). Prove that yn is a Cauchy sequence (and...

By Weierstrass approximation theorem, it seems to be obvious that every continuous function has a power expansion on a closed interval, but I'm not 100% sure about this. Is this genuinely true or there're some counterexamples?

I'm thinking about generalizations of Lagrangian mechanics to systems with infinitely many degrees of freedom, but what I've got uses some extremely sketchy math that still appears to give a correct result. I only consider conservative systems that do not explicitly depend on time. Of course...

I need help with this problem: KleerCo supplies an under-hood, emissions-control air pump to the automotive industry. The pump is vacuum powered and works while the engine is operating, cleaning the exhaust by pumping extra oxygen into the exhaust system. If a pump fails before the vehicle...

Proof about a real-valued continuous function?? Homework Statement Five line segments meet at a point. Show that any continuous real-valued function defined on this set must take the same value three times. The Attempt at a Solution Take the values f(0,0,0) f(0,0,1) f(1,0,0) f(0,1,0)...

Am I correct - First...define the variables - x – Independent variable of the function f. l – The “limit” f(x). The value of l is is known, arbitrary and f(x) should be equal to l. a – a value such that f(a) = l δ – The value of x can be varied by a certain amount...δ is that...

how do i show f(x)=\frac{x}{1-x^2} is a continuous function by means of an \epsilon - \delta proof? oh and x \in (-1,1) so far i have said: let \epsilon>0, \exists \delta>0 s.t. |x-x_0|< \delta. now i need to show that |f(x)-f(x_0)|< \epsilon. yes? can't do the rest of it though...

So, a certain discussion occurred in class today... If f is differentiable, is f ' continuous? At first sight, there seems no reason to think so. However, we couldn't think any counterexample. It also seems logical that f' is continuous since otherwise f wouldn't be differentiable. For...

I don't understand how in quantum mechanics we have discrete and exact energy states for electron orbits but then at the same time we have a continuous probability density function for the position of an electron. This seems like a paradox (although I know it can't be) since considering a...

Whether or not time is discrete or continuous is unknown, and is a key idea answer that many physicists are looking for. This topi is for discussing the factors that effects whether or not ime is continuous, and effects it might have. Before i talk about whether or not time is discrete or...

Prove Sin(x):R--->R is continuous Homework Statement Prove that Sin(x) from R to R is continuous using the epsilon delta definition of continuity and the following lemma: denote the absolute value of x by abs(x) Lemma: abs(x)>=sin(x) Homework Equations Could somebody please just...

Homework Statement For what positive values of b is f continuous for all real numbers x? f(x) = ((x-1)(x2-4))/(x2-b) So I go one value of b for the function to be continuous. I got that b=4. How do I find any others? If there even are any others?

Homework Statement Prove the set of continuous functions from R to R has the same cardinality as RHomework Equations We haven't done anything with cardinal numbers (and we won't), so my only tools are the definition of cardinality and the Schroeder-Bernstein theorem and its consequences. I...

Homework Statement Let f be the function given by f(x)= (x-1)(x²-4)/ (x²-a). For What Positive Values of a is f continuous for all real numbers x? Homework Equations The Attempt at a Solution What I tried doing was separating the (x²-4) into (x+2)(x-2) then moving along from...

Homework Statement Let \[f(x)=\begin{cases}{} \frac{6a(x^2+1)}{2x^2+1}+\frac{b\log \big((x+1)^4\big)}{x} &\mbox{if } x<0,\\ -2a-4 &\mbox{if } x=0, \\ \frac{a\sin x}{x}+b &\mbox{if } x>0. \end{cases}\] Find \(a\) and \(b\) such that \(f\) is continuous at \(x=0\). Homework...

Geometry both discrete and continuous at once, like information--Kempf It is possible for a geometry to be both discrete and continuous. We don't know if our universe's geometry is like that, but it could be. Video of a talk at Perimeter by Achim Kempf, describing this, was put online...

If f and g are continuous functions with f(4)-5 and lim [5f(x) -g(x) ]=5 find g(4) x-->4

Hallo, What is the condition for partial derivatives to be continuous (if I have function f(x,y))? Thanks, Omri

Hello, I would like to get an opinion from somebody on a theory I find interesting. If a fruit fly were to live in a house; and only discreetly eat that which is necessary for survival, It is possible that it could remain unnoticed to a point where it may live comfortable for the rest of its...

I am confused with sequence and continuous functions. I am confued with their limit. how do they know the min and max before they attempt the question. and is that the only solution to the question? I mean. Everytimes if I see kind question like this, is that only way to do it?... Many...

since dirac delta function is not a literally a function but a limit of function,does it mean that dirac delta function is continuous and differentiable through out the infinity? is there any example of dirac delta function if yes then give meeeeeeee?

Hi All, I can't see how the following is proved. Given two topological space (X, T), (Y, U) and a function f from X to Y and the following two statements. 1. f is continuous, i.e. for every open set U in U, the inverse image f-1(U) is in T 2. For every convergent filter base F -> x, the...

Dear friends, I am a new member of physics forums, so this is may new message. Already thanks to you for your helps to my question. I research some applied mathematician problem's numerical solutions. There are initial-boundary value problems. I need an initial condition function which must...

Is a bijective continuous function:[a,b]->[f(a),f(b)] differentiable? I think it has to be. continuity between two distinct values of f(a) and f(b): it got to take all the values between f(a) and f(b) at x in [a,b], by the intermediate value theorem. if f is bijective, at [a,b], f(x) can't go...

I am trying to prove that the bth projection map Pb:\PiXa --> Xb is both continuous and open. I have already done the problem but I would like to check it. 1) Continuity: Consider an open set Ub in Xb, then Pb-1(Ub) is an element of the base for the Tychonoff topology on \PiXa. Thus, Pb is...

Homework Statement For a continuous fibre reinforced polymer, use a diagram to explain how the Young's modulus of the composite varies with fibre orientation and fibre content. Anywhere i could get any of this information? I've been googling with no success for a while

As the thread title. The question is actually: "Given p > 0, find d so that |x-0| < d implies |f(x)-1| < p and hence deduce that f(x) approaches 1 as x approaches 0." My problem is that, when x is near the point x=0, x can be positive and negative, I don't know how to get my delta value because...

i am wondering why k in E(k) diagram is continuous? How is it related to discrete reciprocal lattice which are Fourier components? richard

How to convert a continuous inverse scale parameter into a physically relevant quantity: 1) What is a CISP, and why is called continuous and why inverse? 2) how do I deal with it: Example: On http://www.apec.umn.edu/faculty/gpederso/documents/4501/risk45DistFunc.pdf the error function is...

Lets say I have an equation, y=\alpha e^{\beta W} where, \alpha = a e^{b f} and \beta = c f + d W = \int^{T}_{0}f dt My problem now is, what happen if f is changing with time t, f(t) How do I modify my main equation, y, so that it become an continuous-time function, y(t)...

Homework Statement A subset of A \subseteq R of real numbers is called dense if \forall \delta > 0 , \forall x \in R , \exists a \in A: |x-a| < \delta . Suppose A \subseteq R is dense. Prove that if g is a continuous function with g(x) = 0 for all x \in A , then g = 0 Homework...

Homework Statement Prove that the function f(x) = \sum_{n=1}^{\infty} \frac{cos(n^2x)}{e^{nx^2}2^n} is continuous on R. Homework Equations The Attempt at a Solution I haven't learned about a series of functions converging to a function yet, but would it be sufficient to show...

Homework Statement Determine whether the function is continuous, piecewise continuous or neither on the segment [0, 10] and sketch the graph of f(t). f(t)= {10-t, 0<=t<=8 and 10, 8<=t<=10) The Attempt at a Solution I would say that it was neither as the right hand limit at t = 8...

[b]1. Suppose that f and g are continuous functions defined on R and every interval (a, b) contains some point y with f(y) = g(y). Show that f(x) = g(x) for every x in R. [b]3. I can show that between any two points in are there is some x such that f(x)=g(x). Is that enough? I don't think...

How are continuous space and continuous spectra of operators mathematically consistent with Planck units? Shouldn't the quantum spacetime be a lattice (or what have you) of integer multiples of the Planck length?

Under which conditions is an inverse of a continuous bijection continuous? I'm not seeking for "the" answer. There probably are many. But anyway, I'm interested to hear about conditions that can be used to guarantee the continuity of the inverse. So far I don't know anything else than the...

Hi all, First a warning: my Mathematica skills, and computery-type skills in general, are not very hot. My problem is thus: I have a function which I know: \hat{f}(k) I'd like mathematica to approximate the inverse Fourier transform of this function for me and plot the result. I've...

Homework Statement Suppose f is continuous, f(1) = 5, and f(nx) = [f(x)]^n where n is any integer and x is any real number. Prove that f(x) = 5^x for all real x.Homework Equations The Attempt at a Solution I've proved that f(x) = 5^x for rational x. Now I have to extend this to irrational x...

Homework Statement Suppose f is differentiable on J, c is in J0 and f'(c) > 0. Show that if f' is continuous at c, then f is strictly increasing on some neighborhood of c Homework Equations Strictly increasing: If x < y then f(x) < f(y) Continuous: For all epsilon > 0 there exists a...

I was just reflecting upon my math courses and wondered why can we transform any piecewise continuous functions by using transforms such as laplace transforms or converting to Fourier series by simply adding the required integrals on the respective bounds?

fx,y = 6(x-y)dydx, if 0<y<x<1 how do you find E(XY), i know the formula...g(x,y)fxy(x,y)dydx but i don't know what 'g(x,y)' represents and the limits to use??

Suppose that f: [a,b] \rightarrow \mathbb{R} is continuous and f(x) \geq 0 for all x \in [a,b]. Prove that if \int^b_a f(x)dx=0, then f(x)=0 for all x \in [a,b]. Attempt I had attempted to do this problem by contradiction, except I did not understand how to finish the problem. I would...

Hello, In my QM class last semester, I produced a proof that wave functions must be continuous (used for boundary conditions, etc.) It was an undergraduate level course, so I don't know how easy it would be to do if you had more in the way of theory... But I've been wondering lately...

http://www.vias.org/physics/bk4_06_07.html This is a quote from the mentioned website, " For example, a charged metal ball will have charge spread nearly uniformly all over its surface, and in for most purposes it will make sense to ignore the fact that this uniformity is broken at the atomic...

Hello,I need some advice on a problem. Let f,g:R\rightarrow R (where R denotes the real numbers) be two continuous functions, assume that f(x) < g(x) \forall x \neq 0 , and f(0) = g(0).Define A = \left\{(x,y)\neq (0,0): y< f(x),x \in R\right\} B = \left\{(x,y)\neq (0,0): y> g(x),x \in...