Existence Definition and 543 Threads

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 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...

I was trying to go about deciding whether a planet such as the following could exist: It has a radius of only 2m. It has an acceleration rate of 9.8 m/s^2 (gravity) This way, you can walk on it, and at the same time, you could see whether you were "upside down", although, physically you...

Simple question: Let f be a real-valued function defined an open interval U. If f is twice differentiable at u, then f' is continuous at u right? Does that mean that there exists a neighborhood around u where f' exists for all points in this neighborhood?

While it is widely accepted that there is no existence of the aether, what does this say about Dirac's argument which contradicts mainstream belief? This comes about 50 years after it was suggested that there was no aether. Is this a special case? I was told that aether theory is not excluded...

Homework Statement show the initial value problem x(dy/dx)=4y, y(0)=1 has no solution. does this contradict the existence theorem. please explain The Attempt at a Solution it is easy to find out a general solution is y=C*e^(4x), C is a constant. and for any x the right part of the...

Homework Statement Prove that there exists two infinite sequences <an> and <bn> of positive integers such that the following conditions hold simultaneously: i) 1<a1<a2<a3...; ii) an<bn<(an)^2 for all n>=1 iii)(an) - 1 divides (bn) - 1 for all n>=1 iv)(an)^2 -1 divides (bn)^2 - 1 for all...

Is it true that 0.1% of the mass in an uncontrolled nuclear chain reaction gets converted into energy via E=Mc^2? And if this is so, then does the mass technically go to infinity in accordance with the Lorentz transformation before turning into energy?

Homework Statement The theorem for a unique solution to a DE says: Let R be a rectangular region in the xy plane that contains the point (xo,yo). If f(x,y), which = dy/dx and the partial derivative of f(x,y) are continuous on R, then a unique solution exists in that region. Question...

Hi, I don't know if this has been discussed (or is trivial or even silly). I was wondering sometimes there is reliance on indirect proofs in mathematics. I was wondering can it be proven in any case where an indirect proof exists that a direct proof does not?

Homework Statement a) Verify that both y1(t)= 1-t and y2(t)= (-t^2)/4 are solutions of the initial value problem y-prime = (-t + (t^2 + 4y)^(1/2)) / 2 , for y(2) = -1 Where are these solutions valid? b) Explain why the existence of two solutions of the given problem does not...

I had a brief conversation with a professor of mine and he presented, in short an argument against the existence of black holes. I'm sure you've heard it or a variation of it. It goes something like this: An advisor and his student are near a black hole. They are both wearing a watch, the...

Homework Statement Let F(x) = (x-a)^2(x-b)^2 + x. Show that the output \frac{a+b}{2} exists for some value x. Homework Equations Quadratic formula. x^2 \geq 0.The Attempt at a Solution Hmm I've tried setting the two equal but that doesn't look nice (if I multiply everything out). It's easy to...

Homework Statement Given the IVP problem \rm{(1+x^2)^{-1} \frac{dx}{dt} = \frac{\alpha \cdot 2 \pi}{4} \cdot cos(t)} \iff \rm{(1+x^2)^{-1} dx = \frac{\alpha \cdot 2 \pi}{4} \cdot cos(t)} dt Find the maximal solution with the initial conditio condition x(0) = 0. Then alpha is...

Hey my smart *** English teacher is always asking us to try and prove our existence to him... When someone tries to say "Well you can see me can't you?" He'll reply "Have your eyes never deceived you before? Is that lake in the middle of the desert that always moves away from you when you get...

Forgive me if this is a stupid question, I'll be trying to come up to speed over the next few weeks.. I am trying to recall a model of the universe that stuck in my head from a few years ago. -Does space-time's existence rely on the presence of mass? -When people say that space-time...

Assume GL(n,q) is the general linear group of nxn matrices with entries in the finite field with q elements. Define a Singer Cycle to be an element of GL(n,q) of order (q^n)-1. How can we show that such an element always exists? That is, for all n and q. Thanx in advance.

From this site: http://www.angelfire.com/md2/timewarp/sartre.html we read: What is Being? What is Nothingness? How are they related? For Sartre, Being is objective, it is what is. Being is in-itself. Existence, on the other hand, has a subjective quality in relation to human reality...

So I'm studying infinite limits in my calculus text (seemed close enough to good old arithematic to put in general math, though), and the following rule is mentioned: Given two functions f(x) and g(x) defined for all real numbers, when given the quotient f(x)/g(x) where f(c) is not 0 and g(c)...

Homework Statement given this ODE with initial conditions y(1)=0 \[ (x + y^2 )dx - 2xydy = 0 \] Homework Equations solving this ODE gives us \[y = \sqrt {x\ln (x)} \] as we can see this equation is true only for x>=1 in order to use the theorem on existence and uniqueness we isulate...

I remember before reading bits and pieces about how if we have a function of two variables, say f = f(x,y), then it must be true that d/dx(df/dy) = d/dy(df/dx), where the "d"'s are partials. Can anyone guide me to what this theorem is called or to its implications? Also, does it work in...