What is Existence: Definition and 569 Discussions

Hi! I was wondering: is it possible to have a non-orientable surface in 3D which is parametrized by u and v, with u and v periodic (i.e. is it possible to map the torus continuously into a non-orientable surface in 3D?) If so, does anyone have any explicit examples?

P(x) = "x is Provable" axiom 1 : P(x)→x "Statement x can be proven true." 1. (x∧¬x) consider a contradiction 2. x simplification(1) 3. ¬x simplification (1) 4. x∨∀sP(s) addition (2) 5. ∀sP(s) disjunctive syllogism (3,4) 6. (x∧¬x)→∀sP(s) conditional proof (1,5) "Anything is provable if it follows...

Homework Statement Hello, I have a following problem. For a three-qubit state i need to trace subsystem. For this subsystem AB I calculate eigenvalues and eigenvectors. The task is now to determine according the eigenvalues and eigenvectors whether quantum discord in this system is non-zero...

Are systems ever in a pure quantum mechanical state? If they are, is it possible to know the precise pure QM state? The example I am thinking of is the spin of an electron. If we measure the spin about the "z-axis" and find the result to be "up" then we say the electron is in the pure state...

Hello MHB, Integrate \int_0^4 \frac{dx}{(x-2)^3} We are suposed to integrate when x goes from zero to 4 but when x is 2 the integration does not exist so the integrate does not exist as well? Regards, |\pi\rangle

How does it work, exactly? Assume I have a vector field function and I take the curl of it. If I get a curl of zero, then does that guarantee that there is no potential function? And if I get a curl of non-zero, does that guarantee that there is a potential function? I googled this...

Here is the question: Here is a link to the question: Maths: Caluclus > Functions? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Suppose you have an ODE y' = F(x,y) that is undefined at x=c but defined and continuous everywhere else. Now suppose you have an IVP at the point (c,y(c)). Then is it impossible for there to be a solution to this IVP on any interval containing c, given that the derivative of the function, i.e...

The vector potential in classical electrodynamics can be introduced due to the fact that the magnetic field is the vortex: div \vec B = 0 → \vec B = rot \vec A In the four-dimensional form (including gauge) Maxwell's equations look particularly beautiful: \partial_{\mu}\partial^{\mu} A^{\nu} = j...

Greetings, My questions below could be categorized into a mixture of “history of chemistry” and “experimental basis for chemistry”. I’m having difficulty phrasing the questions that I have, so I’m going to start by stating them as directly as I can, and then spend the rest of this post...

[b]1. Let a != 0 and b be elements of the integers mod n. If the equation ax=b has no solution in Zn then a is a zero divisor in Zn The Attempt at a Solution Not sure where to start on this proof, I keep trying to find something using the properties of modular arithmetic but am coming up empty

Homework Statement y''-4y=12x Homework Equations I don't know The Attempt at a Solution http://imageshack.us/a/img7/944/20130207102820.jpg I'm not sure if I did this right, I'm putting this here to make sure. Please respond within 3 hours if you can because it will be due.

Homework Statement Find a solution of the IVP \frac{dy}{dt} = t(1-y2)\frac{1}{2} and y(0)=0 (*) other than y(t) = 1. Does this violate the uniqueness part of the Existence/Uniqueness Theorem. Explain. Homework Equations Initial Value Problem \frac{dy}{dt}=f(t,y) y(t0)=y0 has a...

according to special relativity theory, any object that has relative velocity also has lorenz- contraction L' = L0 *sqrt (1-(v/c^2)) it sounds odd that this is only kind of length contraction known to exist. why there are no other kind of length expansions or contractions, or are them...

Homework Statement Prove or disprove: \exists a binary operation *:\mathbb{N}\times\mathbb{N}\to\mathbb{N} that is injective. Homework EquationsThe Attempt at a Solution At first, I was under the impression that I could prove this using the following operation. I define * to be...

Hello! This question may seem silly. I'm a first year engineering and computer science student, not a mathematics student. I have only recently become interested in prime numbers, factorization algorithms, and prime number finding algorithms. I know only extremely elementary number theory...

Homework Statement given ##A \subset \mathbb{R}## ##f:A \subset \mathbb{R} \to \mathbb{R}^+## considering the function g such that: ##g(x):=\sqrt{f(x)} x \in A## with ##x_0## limit point in A. Prove that if ##\displaystyle \lim_{x \to x_0} f(x)## exists, then ##\displaystyle \lim_{x \to...

Homework Statement Determine for which real values of a,b,c,d this function is differentiable ##\forall x \in \mathbb{R}##: ##f(x):=## ##ax+b ## ## for x\leq1## ##ax^2+c ## ## for 1\leq x \leq2## ##\frac{dx^2 +1}{x} ## ##for x>2.##The Attempt at a...

So this has crept up in another thread in which another member said that the problem they have with my posts is that I always assume some sort of significance. I just kind of wanted to touch on that and see if anyone else thinks the same.* A lot of people have the view point that, the...

Can existence not exist without math?

Hi, I'm reading through a proof of the existence of a nonmeasurable set. I've copied down the proof below more or less verbatim: In particular, I am trying to understand the significance of why ##\alpha## has to be an irrational number. Would the proof not hold if we used any other...

Homework Statement For question 20.18 in this link: http://people.ischool.berkeley.edu/~johnsonb/Welcome_files/104/104hw7sum06.pdf I understand how they got the value 3/2 for the limit, but I don't see where they proved the existence of that limit...because the question is not just...

Homework Statement Let (G,*) be a finite group of even order. Prove that there exists some g in G such that g≠e and g*g=e. [where e is the identity for (G,*)] Homework Equations Group properties The Attempt at a Solution Let S = G - {e}. Then S is of odd order, and let T={g,g^-1...

Homework Statement These questions were on my midterm a while ago. I want to understand this concept fully as I'm certain these will appear on my final tomorrow and I didn't do as well as I would've liked on these questions. http://gyazo.com/205b0f7d720abbcc555a5abe64805b62 Homework...

I am not certain if this is the right location to put this post, but since this is a section for mathematics and my question is one for mathematicians, it will be placed here for now: How would you, as a mathematician, view time? More precisely, do you think time exists? It might be...

The time reversal operator T is an antiunitary operator, and I saw T^\dagger in many places (for example when some guy is doing a "time reversal" THT^\dagger), but I wonder if there is a well-defined adjoint for an antilinear operator. Suppose we have an antilinear operator A such that $$...

Hey guys, let's say I were to define a new mathematical object, a novel type of number for example, and I am trying to determine its various properties (arithmetic, exponential, logarithmic, etc). Now, let's say I am able to use these numbers to produce solutions that agree with expected...

Homework Statement Let an be a bounded sequence and bn such that the limit bn as n→∞ is b and 0<bn ≤ 1/2 (bn-1) Prove that if: an+1 ≥ an - bn, then lim an n→∞ exists. Homework Equations The Attempt at a Solution as 0<bn ≤ 1/2 (bn-1) the sequence bn is...

Homework Statement Let an be a bounded sequence and bn such that the limit bn as n→∞ is b and 0<bn ≤ 1/2 (bn-1) Prove that if: an+1 ≥ an - bn, then lim an n→∞ Homework Equations The Attempt at a Solution no clue :(

Hi everyone! :smile: I'm newbie in this forum, please help me for my question. In differential equation we know that the differential equation has a solution and uniqueness. which is usually called the existence and uniqueness theorem. my question, what is the difference of local existence...

Let $$M$$ be a surface with Riemannian metric $$g$$. Recall that an orthonormal framing of $$M$$ is an ordered pair of vector fields $$(E_1,E_2)$$ such that $$g(E_i,E_j)=\delta_{ij}$$. Prove that an orthonormal framing exists iff $$M$$ is orientable and $$M$$ admits a nowhere vanishing vector...

Homework Statement A group presentation G = (a,b : a^m = b^n = 1, ba = a^db) defines a group of order mn if and only if d^n \equiv 1 (mod m). Homework Equations One book that I read presents a solution in a way of constructing a group of said order by defining associative binary...

Hi, I've been trying to prove that every vector space has a basis. So starting from the axioms of vector space I defined linear independence and span and then defined basis to be linear independent set that spans the space. I was trying to figure out a direct way to prove the existence of...

Homework Statement In this exercice I'm asked to find out if the limif of the function f(x,y) exists. lim (x,y)→(0,0) sqrt(x*y) / (x^2 - y^2) Homework Equations The Attempt at a Solution I've tried to approach it from different coordinates (y=x, y=0, x=0, y=sqrt(x),...) but I...

My question is in regards to systems of ordinary differential equations. One of my research topics right now involves working with some complicated coupled ODEs used to model ecological stuff. Without getting into the details, the model I am working on now has a bad tendency to diverge for...

Homework Statement Let G be a graph containing a cycle C, assume that G contains a path P of length at least k between two verticies on C. Show that G contains a cycle of length at least √k. The Attempt at a Solution Since C is a cycle, there are two paths between a and b. If P...

Hello - A few questions I have after watching Brian Green’s The Elegant Universe – Within the video Dr. Green shows a neat way to view the different scales relativity and quantum mechanics are involved with. He takes an elevator to a top floor to show relativity’s applicable scale. He steps...

Homework Statement Show that for any two Dedekind cuts A,B, there exists a unique cut C such that A+C=B 2. The attempt at a solution In order to prove this, I need to prove the existence and uniqueness of such a cut. For the existence, I started by considering a cut for which this works...

Dirac's conception of the Positron? I have read that Dirac predicted the existence of the positron when trying to combine QM with Relativity. This doesn't make sense to me. How is the positron related to all this?

In those two links it is written that gravitational energy does not exist. http://arxiv.org/abs/0908.3322 http://fqxi.org/community/forum/topic/1371 1. I read these articles, but how it is possible to say more clearly that gravitational energy does not exist? 2. What this means on an example...

Homework Statement #1. If limit[x->a]f(x) exists, but limit[x->a]g(x) doesnt, limit[x->a](f(x)+g(x)) doesn't exist. T/F? (Proof or example please) #2. prove that if f is continuous, then so is |f| #3. f(x) = [[x]]+[[-x]] for what a does limit[x->a]f(x) exist? Where is f discontinuous...

Homework Statement f(x)= xsin(1/x) if x!=0 = 0 if x=0 does the derivative exist at x=0? Can somebody please provide a visual backup of the result? Is this supposed to be a cusp that's why there is no derivative on a continuous function? Homework Equations The Attempt at a...

I have spent a lot of time trying to verify the existence of an alleged scientific article but have not been able to. The only info I have about the article is the following text: Maybe someone here is aware of this article and can provide the source.

I can't understand a statement in a proof in a textbook. I'm going to terminate the proof at the line that I don't understand. Homework Statement Prove that there exists an x \in \mathbb{R} such that x2=2.2. Their proof until line I don't understand For this, we define S:= \{y \in \mathbb{R}...

According to my book, (\exists!x)P(x) is equivalent to (\exists x)P(x)\wedge(\forall y)(\forall z)[P(y)\wedge P(z)\Rightarrow y=z] But I don't see why the variable z is necessary. Wouldn't the following also be correct but shorter and easier to understand: (\exists x)P(x)\wedge(\forall...

Hi, I'm not a materials scientist by any means, but I have a business idea that would involve the use of a washable magnetic fabric. Does anyone know of any such material? If not, does anyone know a good place I might look to find such information? I've tried googling, but I haven't found...

Question about the existence of "Charge" Is it necessary to have a concept of charge apart from mass and electric field? What I mean to ask is for example in the case of an electron, it can be consisdered to have mass and a negative electric field, where is the need to introduce the concept...

Does anybody know where can I find theorem ensuring the existence of minimizers for isoperimetric problems? I also need the proof.

If \lim_{x \to 0}\frac{e^{nx}+e^{-nx}-2cos\frac{nx}{2} - kx^2}{sinx - tanx} exists and finite, then possible values of 'n' and 'k' Homework Equations By far, I have got one equation relating n and k. \frac{5n^2}{4}-k=0 I can simply put choices in there and get answer, but it would be better if...

I was playing trying to work through a proof in Apostol's Calculus and can't quite understand a step noted. This is from chapter 3, theorem 1.35. Every nonnegative real number has a unique nonnegative square root. The part where you are establishing the set S as nonempty so you can use LUB it...