Existence Definition and 571 Threads

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...

I understand that liquid water cannot exists on Mars for extended periods of time because: a) The atmosphere is too thin b) Resulting in a lower boiling point water c) Which leads to sublimification of solid ice into gaseous vapour Quite specifically, I would like to understand the...

Hi! I don't know much about QM. I'm reading lecture notes at the moment. Angular momentum is discussed. The ladder operators for the angular-momentum z-component are defined, it is shown that <L_z>^2 <= <L^2>, so the z component of angular momentum is bounded by the absolute value of angular...

Homework Statement sup problem if f is continuous on [a,b] with f(a)<0<f(b), show that there is a largest x in [a,b] with f(x)=0Homework Equationsi think it can be done by least upper bounds, but i dun know wat is the exact prove. The Attempt at a Solution

I'm working on a proof of the Peano Existence Theorem. It says that: For a continuous ordinary differential equation dx/dt = f(x, t), where x is in R^n and f is continuous on |t-t_0|<=a, ||x-x_0||<=b when you have an initial value, x(t_0) = x_0, then there is a solution on |t-t_0|<= c...

A Discussion of "Existence". I have been reading these forums for many days and recently decided to make an account. I have read a vast array of topics ranging from Quantum Physics/Mechanics to Transcendentalism, to Buddhism and I have also learned of some new philosophies. I figure expanding...

Hi, If A and B are two metric spaces and there exists two onto functions F and G such that F:A->B and G:B->A, is there a way to prove that there exists a bijection mapping A to B?

hi guys, i have been hearing a lot of speculation about planet x / Niburu's orbit taking it through the centre of our solar system in 2012 obviously with catastrophic effects to bio life. the documentaries i have seen on this event have not come sources which i would consider concrete...

Homework Statement Justify for which complex values of a does the principal value of z^a have a limit as z tends to 0? Homework Equations z^a = e^{a log(z)} log(z) = log|z| + (i) (arg(z)) The Attempt at a Solution Lim_{z \rightarrow 0} z^a = Lim_{z \rightarrow 0} e^{(a) (log(z))}...

During one lecture it was mentioned that equations of the form P(x,y)dx+Q(x,y)dy=0 always have at least one integrating factor. But the lecturer didn't know the proof, I've tried using Google but no luck. Anybody can show me the proof? Thanks a lot.

Hi, This topic has been masterfully avoided in my classes, but several proofs of theorems in multivariate calculus use the existence of a parametrization like this: Let f:\mathbb{R}^2\to\mathbb{R}. Then we can write: f(x,y)=g(t)=f(x(t),y(t)) And from this, we can get some interesting...

I have just finished reading a book on supersymmetry that was written in 1999. It explained extensively about the existence of superpartners. As of 199, though, none had been observed. My question is have any been observed in the last ten years? Also has the Higgs Boson been observed in that...

Does the existence of the proton neccessitate the existence of the electron? I think it is strange that the number of electrons is exactly equal to the number of protons at every event level of the universe.

I just had an idea. I'll throw it at you and see if it sticks. What do you think of splitting the word to exist and give it a companion maybe "to besist"? Besist would mean mathematical existence, and the existence of rules. So Numbers besist and Newtons Laws besist, but cake, elephants and...

Let's say that every being in the universe, including me, believed that I could float up into the sky like a soap bubble, would I? Who would be there to say I would not?

For understand general relativity, they tell me, there have flat space, add a sun, the flat space changed to curved space, so the Earth move around. There has a question, if we admit mass, space , time is created, how could exist flat space? there have space-time and there have nothing?

I have been trying to teach myself math, and for quite a while have been struggling through "Calculus on Manifolds" by Spivak. Theorem 2-8, on p.31, uses the Mean Value theorem to establish the existence of the Derivative assuming the existence of the partial derivatives. Doesn't that also...

Apologies, the title messed up - was meant to be 'existence of a C: AC=CA=0 for 2x2 matrices'. Homework Statement How would one show 'nicely' that for any 2x2 non-zero matrix A, there exists some 2x2 non-zero matrix C such that AC=CA=0? I can see how to show it by showing that the determinant...

It has been proven that particles can exist in two or more places instantaneously. Is this ability limited to specific particles or universal?

Existence and Uniqueness of solutions (pretty urgent) Homework Statement I need to solve some problems and I've given one as an example. The question is if there is existence and uniqueness of solutions to the DE Homework Equations u'(x) = sin(u(x)) The Attempt at a Solution I...

Defend your answers. 1) Does the number 1 exist? 2) Is it true that 1 + 1 = 2? 3) Is it possible that 1 + 1 = 2 is false? 4) Can you doubt that 1 + 1 = 2? 5) Can you doubt that 1 exists? 6) Can you prove that a statement is true without knowing the meaning of the statement...

Homework Statement Hi there - I'm wondering about how you can actually show the existence of a scalar potential for an irrotational vector field E - if \nabla \times E = 0 everywhere, then how does one show there exists a scalar potential \phi(x) such that E=- \nabla \phi ? The Attempt at...

Does the existence of an infinite number of universes allow for reincarnation to exist?

Homework Statement Given: For all n > 2, there exists a prime p : n < p < n! (given hint: Since n>2, one has n!-1>2 and therefore n!-1 has a prime divisor p.) The Attempt at a Solution I made an attempt at doing the proof by induction, as the previous question was by induction...

Is 'existence' a concept or an actual state? Does it take a brain and its processing abilities in order to conceptualize an external world? It seems to be true. But, does it take a brain and its processing abilities to actualize an external world? Hmmm... Any takers out there?

I know not far in the past that that largest particle accelerator yet created was set to be activated. Can anyone please give me any information concerning whether or not it was activated and/or the consequences, if any, of what was discovered? Even the name of this contraption and where it is...

Context: In beta-decay the kinetic energy of the electron is continuous. This led Pauli to the conclusion, that the pre-1930 picture (beta-decay = neutron -> proton + electron) is incorrect and he assumed that a third particle (the neutrino) is taking part. Question: Why would the following...

Existence: Consciousness arises from a complex set of physical causes and effects. It is amazing to think that consciousness exists at all, it seems a very out-of-place phenomena within our universe. There are many unique arrangements of matter in the universe, the majority of these are...

Homework Statement For what values does the limit exist? Lim_{n\rightarrow}\infty(\frac{z}{z conjugate})^n Homework Equations The Attempt at a Solution [(x+iy)/(x-iy)]^n I just don't know how to tell when it exists. For even values of n because then there would be no sign changes?

In general, what is a good method to prove whether or not a limit exists? For example limit of sin(1/x) as x approaches zero.

Homework Statement Problem 1 of 2: Why is it that the continuity of a function in a region R and the continuity of the first partial derivative on R enables us to say that not only does a solution exist on some interval I0, but it is the only solution satisfying y(x0) = y0? Problem 2 of...

Homework Statement Let G be a group of order pem. Prove that G contains a subgroup of order pr for every integer r \leqe The Attempt at a Solution By sylow 1 we know that there exists a subgroup of order pe. so that case is done, we need to show that supgroups of order r<e exist now...

Homework Statement Prove that if f(x) is convex on an open interval, then left and right derivatives of f exist at every point. The Attempt at a Solution So i have been able to show (from the definition of convex) that for any x1< x < x2 in the interval: \frac{f(x)-f(x_1)}{x-x_1}\leq...