Existence Definition and 543 Threads

dear friends, i've noticed that the main feature of my inner experience is the sense that something exists, and that the main feature of my outer experience is the sense that something is solid, and I've wondered if these two experiences might be two views of the same thing: solid existence...

the big bang theory suggests that all the matter around us was once infinitely concentrated at some particular high density region...this matter then spread out across the universe following the big bang... but how did this energy/matter come into existence in the first place??..

I'm wondering if there is a monotonically increasing function with a jump discontinuity at every rational (or any other dense, countable subset of the reals). Here's a specific candidate that I've come up with: Let g:\mathbb{Q} \cap [0,1] \rightarrow \mathbb{R} take the rational p/q (p and q...

Homework Statement a) Does f(z)=1/z have an antiderivative over C/(0,0)? b) Does f(z)=(1/z)^n have an antiderivative over C/(0,0), n integer and not equal to 1. Homework Equations The Attempt at a Solution a) No. Integrating over C= the unit circle gives us 2*pi*i. So for at least one...

In your own words, what exactly is the purpose of the Existence Uniqueness Theorem and why is it useful

Hi everyone, Does someone knows where I can the statement about the existence theorem of caratheorory solutions? Thank you

I have a non-linear differential equation and I wonder whether it has a soliton solution or not. How can I approach to the problem? So far I have never dealt with non-linear differential equations, hence, any suggestion is appreciated.

Hi together ... I wonder how one can deduce the existence of antiparticles from the Klein-Gordon equation. Starting from (\frac{\partial^2}{\partial t^2} - \nabla^2 + m^2) \Psi(t,\vec{x})=0 one gets solutions \Psi(t,\vec{x})=\exp(\pm i (- E t + \vec{p} \cdot \vec{x})) leading to E^2=p^2 +...

I'm studying for my numerical analysis final on tuesday, and I know this is going to be one of the problems, so any help is greatly appreciated. Homework Statement State and prove existence and uniqueness for the solution of the linear least squares problem. Homework Equations y \approx...

Imagine that you are an astronaut standing very far from a black hole.Now you throw a luminous body (a bulb may be) directly towards it.Now as it gets nearer the black hole,the light from the bulb as you observe it becomes more red-shifted.Eventually from your frame(consider it is an inertial...

Using the existence and uniqueness criteria, give the region (call it D) in the x-y plane consisting of all points (xo, yo) such that there is a unique solution. Choose a point in D as your initial condition, show that the equation is exact, then use the fact to solve the associated initial...

Hello all, I've recently used a property that seems perfectly valid, yet upon further scrutiny I could not come up with a way to prove it. Here is what I would like some help on. Given two sets X and Y and functions f and g mapping X into Y, with the property that f is injective and g is...

Homework Statement Is there a group of order 12 which contains one involution and ten elements of order 3? Give an example or otherwise prove that such a group cannot exist. 2. The attempt at a solution Let G be a group of order 12 = (p^k)*m where p is a prime number, k is greater than or...

Let f be a continuous on the closed and bounded interval [a,b] and x_1, x_2, …, x_n ∈ [a,b]. Show that there necessarily exists ξ ∈ [a,b] such that: f (ξ= [f(x_1) + f(x_2) + …f(x_n)] / n How can I start this problem i am really confused! please help !

Homework Statement Let's take function given by a condition: f(x) = \begin{cases} \frac{1}{q^2} \ iff \ x = \frac{p}{q} \ $nieskracalny$,\\ 0 \ iff \ x \notin \mathbb{Q} \end{cases} Prove the existence of the derivative of f in all points x \notin \mathbb{Q}. The Attempt at a...

I wonder if anyone knows or can figure out an answer to this question I've been thinking about: In a smooth pseudo-riemannian manifold like those in GR, and given some arbitrarily long spacelike geodesic, is it always ( or almost always, e.g. except for passing through a singularity) possible...

How we can prove the existence of black holes? And how they are located in in the space as they can absorb light too?

Homework Statement Just a clarification: the two last equations must hold in an open neighborhood of the point (2, 1, -1, -2), not just at that point. Homework Equations The Attempt at a Solution I have to do an existence proof. The shortest way of accomplishing this would...

Homework Statement Let k be any positive integer. Prove that there exists a positive integer multiple n of k such that the only digits in n are 0s and 1s. (Use the pigeonhole principle.) Homework Equations The General Pigeonhole Principle If more than mk things are distributed into k...

Unintelligent Design theory Take a look at the Sun (with proper darkened glasses of course). Have you ever wondered why is it there? In fact there are so many other places it could be (other galaxies, etc.) that it is quite improbable it is there. Therefore someone, let's call him the...

Here is a potentially neat problem. Let x(t),y(t) (for all t\in \mathbb{R}) be polynomials in t. Prove that for any x(t),y(t) there exists a non-zero polynomial f(x,y) in 2 variables such that f(x(t),y(t))=0 for all t. The strategy is to show that for n sufficiently large, the polynomials...

Do electric and magnetic fields occur simultaneously in the same spot anywhere around the globe? (other than during solar flares) If the field is named "electromagnetic" wouldn't that means exactly this simultaneity? Thank you.

Let V be a finite-dimensional vector space over the field F and let T be a linear operator on V. Let c be a scalar and suppose there is a non-zero vector \alpha in V such that t \alpha = c \alpha. Prove that there is a non-zero linear functional f on V such that T^{t}f=cf, where T^{t}f=f\circ T...

Given the equation y'= xg(x,y) , suppose that g and (partial) dg/dy are defined and continuous for all (x,y). Show the following: 1) y(x)=0 is a solution 2)if y=y(x), x in (a,b) is a solution and if y(x0)>0, x0 in (a,b), then y(x)>0 for all x in (a,b) Please i need your help.

Homework Statement Let T be a family of finite subsets of the natural numbers N = {1, 2, 3,...} such that if A and B are any members of T, then the intersection of A and B is nonempty. (a) Must N contain a finite subset F such that the intersection of A, B and F is nonempty for any sets A...

Example of a "pure existence metaproof" http://en.wikipedia.org/wiki/Existence_theorem A pure existence theorem is a theorem which states the existence of something, but the proof of the theorem does not indicate a construction of the thing in question. As the article mentions, this is...

Homework Statement Prove or disprove a) Let f:X---->Y. If f possesses more than 1 left inverse yet has no right inverse, then f has strictly more than 1 left inverse. b) If f and g are maps from a set X to X and fog is one to one, then f an g are both injective one to one. Homework Equations...

Prove that there exist (a) 5 points in the plane so that among all the triangles with vertices among these points there are 8 right-angled ones; (b) 64 points in the plane so that among all the triangles with vertices among these points there are at least 2005 right-angled ones.

Homework Statement I have set up this problem for myself. Let P be a system of the form x' = Ax + Bu y = Cx + Du The definition of a "state" is: "x(t) is a state for a system P if knowledge of x at some initial time t_{0} and the input u(t), t \geq t_{0} is sufficient to uniquely determine...

Imagine viewing the world from state X at 1 pm, and viewing the world from state Y at 2 pm. State Y is required to be in existence in principle at the viewing of state Y, and at state X equally. This is because neither is more valid of a state to view the world from. Neither can claim it is more...

A torch (flashlight US) is positioned on a train going at 70kms/hour. Relative to someone standing beside the train track the torch will have a velocity of 70kms/hour since it is on the train. When you switch on the torch, a light beam emanates. However, the light was not actually inside the...

It is easy to see, from bianchi identities, that if energy-momentum tensor is not conserved, then Einstein's equation does not have a solution. But is there a proof that if energy momentum tensor IS conserved then Einstein's equation ALWAYS have a solution?

Homework Statement Coeffcient Data and Existence and Uniqueness of Solutions. Assuming that a (not equal to) 0, and an equation that restricts a; b; c; d so that the following system has only the trivial solution. (1) ax1 + bx2 = 0 (2) cx1 + dx2 = 0 Hint: Find the echelon form of the...

In the another thread, I queried some posters comments which were along the lines that zero is a metaphysical concept / doesn't exist. Baywax responded, as below, and my additional comments are in blue. Zero exists as much as the number 1 in that these are both language equivalents that...

While reading C.C.Pugh's "Real Mathematical Analysis" I've encountered a following statement: "A starlike set U \subset \mathbb{R}^n contains a point p such that the line segment from each q\in U to p lies in U. It is not hard to construct a diffeomorphism from U to \mathbb{R}^n." It's little...

what is quantum chaos? dose it exist realy? the original definition of classical chaos is a system with exponential sensitivity to initial conditions. however in quantum mechanics because of the linear property of the schrodinger equation, variation on initial condition of the wave function...

(In the following discussion, when I use the word "always", I mean "as good as always" if you're willing to ignore exotic systems with negative temperature and such) In the following discussion I will assume we're working in a heat bath with constant T and P: So there are several ways to see...

Is it possible for a black hole to exist in a reference frame and not exist in another? I did some naive calculations and the result was that what are neutron stars in relation to Earth could be black holes in relation to a proton accelerated near the speed of light at LHC. That is because...

how do we "know" it must exist? btw I am new here, don't flame me too hard

Homework Statement "Given a function H, assigning a value, 0 or 1, to each atomic sentence, define a sequence ℑ0, ℑ1, ℑ2, ℑ3,... of functions, as follows: ℑ0 is just H. Given a function ℑn, assigning a value, either 0 or 1, to the sentences of degree less than or equal to n, define the...

i'm new here and I'm not sure if this has been asked before, but I'm just wondering about the cause of its existence. I'm speculating that it may be caused by interaction between a proton and electron together with their masses, if so, how?

Homework Statement Consider the initial value problem \begin{align*} \left\{ \begin{array}{l} \displaystyle \frac{dy}{dx} = \exp(xy) \\ y(0) = 1 \end{array} \right. \end{align*} 1. Verify that this IVP has a unique solution in a neighborhood of x = 0. 2. Following the...

Most functions y=f(x) have tangent lines for any point x. Does a function z=f(x,y) have a tangent plane for any point x,y? And could you extend this to higher dimensions if necessary? (Tangent cubes? Tangent hypercubes?) Edit: Sorry, I thought I was posting in the General Math forum...

To my layman-ey thinking light is the only thing in existence you can define by the fact that it is only ever moving, can never be stationary. Is there anything else in existence sharing this property? Otherwise this makes light very, very weird in a unique/special way?

G,H be groups(finite or infinite) Prove that if (G:H)=n, then there exist some normal subgroup K of G (G:K)≤n! example) let G=A5, H=A4 then (G:H)=5, then K={id} exists, (G:K)≤5!

(sorry if this is in the wrong section, or if this does not belong on these forums) A friend of mine told me a while back that although the location of Atlantis is unknown, it is likely that it existed in the middle of the Seven Wonders of the World. (I naturally assumed he meant the Seven...

Earlier today, I was thinking about the statement that "there exists no greatest natural number" and immediately, two proofs sprang to my mind. Since my question depends on these, I'll write them out below . . . Proof 1: Let n \in \mathbb{N}. Clearly n+1 \in \mathbb{N} and n < n+1. Since...

Is it possible that the universe we live in has a ciclyc way of existing? I mean,could our universe born with te big bang,then expand,stop expanding,to slowly attract matter in one point than implode;and after all this to explode again in another big bang?

I watched the trailer for the PBS documentary "Into God - The Closer To Truth," and it seems like something I want to see when it becomes available. It will be shown on the "Closer To Truth [Cosmos, Consciousness, God]" program. The trailer for "Into God" is at: http://www.vimeo.com/6163114...

Homework Statement Given this ODE: x' = x+y-xy^2 y' = -x-y+x^2y and a function: u(x,y) = x^2+y^2-2ln|xy-1| prove that for each soloution ( x(t), y(t) ) of this system, such as: x(t)*y(t) != 1 (doesn't equal...) , there exists a constsnt C such as: u ( x(t), y(t) ) = C for every t in...