Existence Definition and 570 Threads

Homework Statement Suppose f(t,x) is a continuous vector valued function on \mathbb{R} \times \mathbb{R}^n. If f is locally Lipschitz with respect to x with the property that \|f(t,x)\| \le C \|x\| for some positive constant C > 0, then prove that the maximum interval of the existence of the...

I have recently been studying Gregory Chaitin's "algorithmic information theory" for a school project. It describes the complexity of mathematical objects by the size of the smallest Turing machine program capable of computing them (in bits). It also defines a "random" object as one with an...

From what I understand, vacuum energy is a form of energy that exists in freespace, even when completely devoid of matter. So, I have two questions: 1. Can vacuum energy exist if there were no matter anywhere in the universe? 2. If so, where does this vacuum energy come from?

Are we sure about the existence of virtual particles?

Hello, I just reading and learning QFT and there is something I've been wondering, hopefully somebody here can help me. Let's say we have an interacting Quantum Field Theory, such as Quantum Electrodynamics if we want to compute an amplitude such as two electrons scattering off each other, then...

What is "existence" and what will it mean to "exist" ? What will it mean that I (eventually) does exist ? What will it mean that something outside me exist as observed by me ? What will it mean that something outside me exist as I does not observe it ? What is then "exisistence" ...

Wiltshire casts doubt on existence of "dark energy" Wiltshire is a minority voice in cosmology, but one worth listening to. Speculation about a "dark energy particle" would be in vain if the appearance of acceleration can be traced to classic GR effects, which is what he tries to do. Wiltshire...

I would like to find a proof for the existence of the instantaneous center, and show that it only exists for velocity and not acceleartion. Anyone know where I could find this proof.

Hi everyone I'm currently readig Bruce Rosenblum & Fred Kuttner's book Quantum Enigma: Physics Encounters Consciousness and studying to be an NLP practitioner as well as practising tai chi. There are lot more parallels in these three areas than I imagined there would be. I have a few...

According to Klein Kaluza theory of fifth dimension (followed by string theory), there is an elecromagnetic dimension in which every particle of Universe (in Dirac Vacuum) perform translatory and rotational motion due to which they drag the e-m dimension. Thus if any two particles are placed...

I have been recently introduced to the idea of Jordan form of a matrix, and I have attempted to prove it. However, there is one step that I cannot prove. If I can prove the step, then everything else is done. Let A be a m by m matrix with characteristic polynomial ch(x)=(x-\lambda)^{m} I want...

Homework Statement A plane is colored blue and red in any way . Prove that there exists a rectangle with vertices of the same color Homework Equations Its obviously true. The Attempt at a Solution I was thinking proofy by pig hole, but haven't quite figured it out.

i need to prove diprove that there exist matrices A1,A2,...,As such that rank Ai=1 for every i=1,...,s and A=A1+A2+...+As with rankA=10. my feeling this is not true, i thought trying to prove this by ad absrudum, let us assume that they exist, then the rows of Ai are scalar multiple of one row...

I'm reteaching electrodynamics to myself on a more rigorous footing, and I'm trying to prove to myself that setting the divergence of the vector potential is justified using a gauge shift. I could use the Helmholtz theorem to do this, but the problem with this from my perspective is that I...

RE: Thoughts on existence (& happiness) Sorry I'm not sure if its o.k. to continue a thread, I just find this an interesting subject because it's such a basic question. What are peoples reasons for living from one day to another? Not only as individual humans but as a whole specie. I'm not...

This poll presents these options "I experience life as a physical phenomenon" and "I experience life as a non - physical phenomenon" and will include the obligatory third option of "all of the above" and the 4th choice "I experience life in a way other than physical, non-physical and not...

There are certain possibilities for the form of existence from my point of view but one of these possibilities seems to be really logical and sounds very likely to be true which is given as follows I'd be glad to receive your comments on this subject; Let’s imagine two astronomers traveled...

hello I'm new. I'm 27/m/ USA. I'm interested in trying to explain existence. i am hoping to start a thread where we all try. I've been studying and trying for a long time but have never shared my conclusions. so i guess i'll start ...hopefully we can all just keep adding on and reach the...

Greating my friends, I have just returned home today from heart surgery. I still feeling the effects of the operation, because I'm affried the hospital send me home a bit to early. But I have to have these questions finished before tomorrow. So therefore I would very much appreciate...

Hi, For a first order Diff Equa. x'=f(x,t) and the IC: x(0)=x_0. with t from [0 to infinity) If f(x,t) doesn't satisfy the Lipschitz condition, can I say for sure that there doesn't exist a global unique solution? I think the answer is "no" but I am not sure. Can you all confirm...

In the name of God The Source of our Existence Civility Introduction Chapter I: Civility Chapter II: Adam and Eve Story of Paradise Chapter III: Moses Story is a Fiction Chapter IV: Christianity in Crisis Chapter V: A Plausible Philosophy of Soul...

Prove that if b is greater than or equal to zero (b in R), there exists a non-negative real number x such that x2=b. I really don't know where to go. I think I need to modify a proof done in a class that I missed, so if someone could just give me a few hints I'll fill in the rest. Thanks Josh

Let be the integrals: \int_{-\infty}^{\infty}dx Cos(uf(x)) (or the same but a sine) and \int_{-\infty}^{\infty}dxe^{-ag(x)} Where "a" is a a>0 positive constant, u can be either positive or negative.. and g(x)>0 for every real x.. my question is will these integrals "always2 exist...

Hello, I would be glad to know your point of view on the following idea of mine :smile: , I'll be happy to have links for or against this idea. Thankyou for giving the time ________________________________________________________ Whenever I start thinking about the existence of the...

Can we agree that "all existents can be measured" ? By existent we mean "an entity (thing) of a specific nature made of specific attributes". By measurement we mean "the identification of a relationship between an attribute of an entity and a standard that serves as a unit". Thus can we agree...

Just wondering a few wonders out (i don't have much knowledge about physics and stuff, just the basics, so don't expect me to not ask questions that don't make sense to some, or to know answers that should be obvious). Just too much thinking time on my hands. First, just wondering if a test...

In studying physics and as much literature as I can possibly get my hands on I have come to a theory as to why everything from bosons and quarks up to conscience human beings exists. The simplicity of the concept suprised me but when I tried applying it to every level inbetween I can not find...

About a year and a half ago I came to the decision that I'm no longer christian. Since then I've been studying every source that has anything to do with our beginning. Its through my study of physics and cosmology that I've finally come to my belief in our origins. In the bible it says that...

The recent topic is about existence.I do not want the precise deinition.But, want to know clearly, what does it mean.

I was surfing some old exam questions and I found a nasty one... They asked to prove the existence of fringe effects of the electric field at the edges of a plate capacitor, using Maxwell's laws. In class we always assumed the ideal capacitor without fringe effects so I'm having some kind of...

Need help with ODE and "Existence and Uniqueness Thm" I'm currently helping my neice study for her exams and going though last years test there was this one question that I wasn't sure about. ------------- Considering the initial value problem, \frac{dy}{dx} = f(x,y) Where f(x,y) = (1+x)...

I have a harsh realistic philosophy. I enjoy it too. I am a atheist, and do not believe in any "super natural power" such as a "God." I know that science has its laws and that we were created by some chemical process. Humans contribute nothing, nor is there anything to contribute too. The...

i have some question and i hope i put this topic in the right thread.. >> is there any philosophy or science maybe that until now has not yet been discovered that could serve as an answer to the question about on how all things in the universe [including us] came into existence. For me i...

Lin Alg - Eigenvector Existence proof (More of a proof ?, than eigenvector ?) Here is the question from my book: Show that If \theta \in \mathbb{R}, then the matrix A = \left(\begin{array}{cc}cos \theta & sin \theta \\ sin \theta & -cos \theta \end{array}\right) always has an...

When nothing exists, nothingness exists. (Because I'm alive and we use words.) If so, existence exists. Is there a state where existence doesn't exist? Is there a state where nothingness doesn't exist? When I die, will nothingness continue to exist? When I die, will existence...

"Suppose V is an n-dimensional vector space over an algebraically closed field F. Let T be a linear operator on V. Prove that there exists a cyclic vector for T <=> the minimal polynomial is equal to the characteristic polynomial of T." (A cyclic vector is one such that (v,Tv,...,T^n-1 v) is a...

My friend and I were having a discussion about human existence and sentience, and an interesting idea for an experiment came up. Suppose two genetically identical people of the exact same age and parentage were raised in two identical rooms separated from all living things. There are no...

This is my first post here, so I appologise in advance if this is the wrong forum. Anyway, I was interested to see if this was a generally held opinion. My philosophy course didn't really go into much detail (alas, only Higher level (in Scotland)) I think that the cosmological argument goes as...

Let G \subset \mathbb{R}^{n}\mbox{ open } a \in G f : G \rightarrow \mathbb{R} f \in C^{1}(G) Df(a) = \overrightarrow{0} Then: (i) if D^2f(a) is positively definite, then f has local minimum in a (ii) if D^2f(a) is negatively definite, then f has local maximum in a (iii) if...

Short question: Can anyone provide me with a nice synopsis of how to go about proving the "existence" of some object as often requested in math questions such as, "prove that X really exists and is unique"? In other owrds, in general, when presented with an "existence" question, is there a nice...

The question of reality, existence and philosophy in general is (as most of us would agree on, I assume) based on human brain activity. We think with our brains, we process EVERY INPUT of information from this "existence" or "reality" or whatever you want to call it with our brains and generate...

Hello, For clarification because of the ambiguous situation in searching for & concerning the Higgs Field. It is with 95% confidence that the Higgs Field exists. Yet it has not been seen as of the end of 2005. I hope LHC/CERN will shed light on the subject. Anyone dealing or knowledge...

is it mathematicly/statisticly impossible for the universe and existence (i'm talking from the moment of the big bang to when life first appeared) to have happened randomly? so many billions and billions of thing's had to happen just right from the big bang to when life first appeared without...

A common argument: Suppose God is all-powerful. Now, let God create a rock so heavy that God cannot lift it. Common conclusions: 1) But if God cannot lift it, then God is not all-powerful. 2) The rock cannot exist since it creates a contradiction. Thus, God is not all-powerful since...

lets say theoretically you have a rope 200,000 miles long and it was pulled tighted with a person on each end one persons pulls the rope towards them instantaneously the rope begins to leave the other person wouldn't this conclude that something is faster than the speed of light?

does nothing exist apart from my mind?

Can anybody help me with the proof of Existence and Uniqueness Theorems.

As I understand it, according to the Copenhagen interpretation of QM, nothing can be said to exist until it is observed. I have also read that it is impossible to observe virtual particles in an experiment. How is it then that virtual particles can be said to exist?

Hi, Do white holes exist? If not why not? If a white hole is the opposite of a black hole then it will have the following properties:- Black holes converge, localise or attract matter towards a point. white holes diverge, non-localise or repel matter. White holes should therefore be called...

prove that between any two real numbers there is a number of the form \frac{k}{2^n} where k is an integer and n is a natural number.