Theorem Definition and 1000 Threads

Consider a point A outside of a line α. Α and α define a plane.Let us suppose that more than one lines parallels to α are passing through A. Then these lines are also parallels to each other; wrong because they all have common point A.

I've been slowly grinding away with what I can about quantum mechanics and QFT. I'm not sure how far I've gotten but I've come up against a bit of a roadblock concerning how the relativity of simultaneity applies in QFT with specific reference to the outcome of Bell tests. My misunderstanding...

I am reading Stephen Willard: General Topology ... ... and am currently reading Chapter 2: Topological Spaces and am currently focused on Section 1: Fundamental Concepts ... ... I need help in order to fully understand an aspect of the proof of Theorem 3.7 ... ..Theorem 3.7 and its proof...

In the general expansion of (1+x)^n what does the sum of the coefficients mean?

hi guys our solid state professor gave us a series of power point slides that contains the derivation of Bloch theorem , but some points is not clear to me , and when i asked him his answer was also not clear : in the first part i understand the he represented both the potential energy and the...

Hi, I just have a quick question about a problem involving Gauss' Theorem. Question: Vector field F = \begin{pmatrix} x^2 \\ 2y^2 \\ 3z \end{pmatrix} has net out flux of 4 \pi for a unit sphere centred at the origin (calculated in earlier part of question). If we are now given a vector...

To my mind, there are two distinct approaches to energy problems that different authors tend to use, and I wondered whether either is more fundamental than the other. The first is variations on the work energy theorem, and the second consists of defining a system boundary and setting the change...

Let ##S_t## be a uniformly expanding hemisphere described by ##x^2+y^2+z^2=(vt)^2, (z\ge0)## I assume by verify they just want me to calculate this for the surface. I guess that ##\textbf{v}=(x/t,y/t,z/t)## because ##v=\frac{\sqrt{x^2+y^2+z^2}}{t}##. The three terms in the parentheses evaluate...

$10 min = \dfrac{h}{6}$ So $a(t)=v'(t) =\dfrac{\dfrac{(50-30)mi}{h}}{\dfrac{h}{6}} =\dfrac{20 mi}{h}\cdot\dfrac{6}{h}=\dfrac{120 mi}{h^2}$ Hopefully 🕶

Hello Guys, I really need help, I am trying to simplify this circuit to calculate Rth and I got stuck.

In deriving the work-energy theorem, Griffiths does the following: ##\frac{d\mathbf{p}}{dt}\cdot\mathbf{u} = \frac{d}{dt}\bigg(\frac{m\mathbf{u}}{\sqrt{1-u^2/c^2}}\bigg)\cdot\mathbf{u}=\frac{m\mathbf{u}}{(1-u^2/c^2)^{3/2}}\cdot\frac{d\mathbf{u}}{dt}## I may have forgotten something essential...

Ok Just have trouble getting this without a function..

$\tiny{3.2.15}$ Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. Graph the function the secant line through the endpoints, and the tangent line at $(c,f(c))$. $f(x)=\sqrt{x} \quad [0,4]$ Are the secant line and the tangent line parallel...

My try: I tried to take the expression for the decomposition coefficients and put it into the equation that I had to prove. Then, I tried to work with the integral limits in order to get into Wiener-Khinchin theorem or maybe Fourier transform of delta function but I didn't see any success in...

I have been following the proof of the Stone's theorem on one-parameter unitary groups. The question is if the current list of self-adjoint operators used in quantum mechanics, including position and momentum operators, is exhaustive or not? Put it another way, can we say that there is no...

My attempt: According to the implicit function theorem as long as the determinant of the jacobian given by ∂(F,G)/∂(y,z) is not equal to 0, the parametrization is possible. ∂(F,G)/∂(y,z)=4yzMeaning that all points where z and y are not equal to 0 are possible parametrizations. My friend's...

I am reading Tej Bahadur Singh: Elements of Topology, CRC Press, 2013 ... ... and am currently focused on Chapter 1, Section 1.2: Topological Spaces ... I need help in order to fully understand Singh's proof of Theorem 1.3.7 ... (using only the definitions and results Singh has established to...

The proof for the ET I've found in some of the undergrad books for statistical physics (for example in Reif's "Statistical and Thermal Physics") assumes the form of the Hamiltonian of the system to be: $$H = bp_i^2 + E'(q_1,...,p_f)$$ where ##b## is a constant. My professor in his notes, says...

The CHSH version of Bell's theorem uses a digitization to obtain integer results in the set made of 1,-1, and then sums 4 of them. Could it be that digitizing after the sum gives a higher result since for example instead of subtracting 1 one would subtract only .2 for example ?

I do not understand how can I parameterize the surface and area and line differentials.

Hi, I have a quick question about part 1 of this upper bound theorem question (in the attached image). Answer says that \lambda_c = 2.25 . First, we know that there is 1 redundancy and therefore there will be a maximum of 2 plastic hinges for failure. I have found that there needs to be...

I am reading Cesar E. Silva's book entitled "Invitation to Real Analysis" ... and am focused on Chapter 4: Continuous Functions ... I need help to clarify an aspect of the proof of Theorem 4.2.1, the Intermediate Value Theorem ... ... Theorem 4.2.1 and its related Corollary read as follows...

I have already proved that for a graph $G$ with $n$ vertices and $|E(T'(n,q))|$ edges, $\alpha (G) \geq q$. Additionally, if $\alpha (G) = q$ then it must be that $G \cong T'(n,q)$. Apparently this is the "dual version" of Turan's Theorem. How does this theorem imply Turan's? That $ex(n...

I know in 1939 Wigner published a theorem that all fields must be tensors from a couple of books, but can't find the proof anywhere. That obviously is an important result so does anyone know where I can find the proof? Another I haven't seen the proof of is the no interaction theorem. I wish...

The fundamental theorem of arithmetic applies to prime factorizations of whole numbers. Can this theorem also correctly be invoked for all rational numbers? For example, if we take the number 3.25, it can be expressed as 13/4. This can be expressed as 13/2 x 1/2. This cannot be broken...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 3: Continuous Functions on Intervals and am currently focused on Section 3.1 Limits and Continuity ... ... I need some help in understanding the proof of Theorem 3.16...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 3: Continuous Functions on Intervals and am currently focused on Section 3.1 Limits and Continuity ... ... I need some help in understanding the proof of Theorem 3.16...

Hi. I'm trying to grasp what the PBR theorem is about. I'm not tackling the full version, but rather the simple example in @Demystifier's summary. While I think I understand the mathematical steps, my question is why you need two systems to prove it. Is this only technical or more fundamental...

Hi all, I would like to know if in proving the Catalan's conjecture Preda Mihailescu used the infinitude of primes. Best wishes, DaTario

##0=1+a+b+c## ##20=8+4a+2b+c## it follows that, ##13=3a+b## and, ##0=k^3+ak^2+bk+c##...1 ##0=(k+1)^3+a(k+1)^2+(k+1)b+c##...2 subtracting 1 and 2, ##3k^2+k(3+2a)+14-2a=0##

Hi, My question pertains to the question in the image attached. My current method: Part (a) of the question was to state what Stokes' theorem was, so I am assuming that this part is using Stokes' Theorem in some way, but I fail to see all the steps. I noted that \nabla \times \vec F = \nabla...

I have a problem which consist in 1 bit RAM made of 3 MOSFETs. One of the questions is to calculate the maximum voltage that the memory element can receive. I have obtained the result by inspection (it is 4 Volts) but I'm unable to reach the same by applying the Thevenin Theorem. My...

I tried to derive the right hand side of the Radon-Nikodym derivative above but I got different result, here is my attempt: \begin{equation} \label{eq1} \begin{split} \frac{\mathrm d\mu_{\Theta\mid X}}{\mathrm d\mu_\Theta}(\theta \mid x) &= f_{\Theta\mid X}(\theta\mid x) \mathrm \space...

Although Stokes Theorem says that the line integral of a closed surface equals to zero why do we get a non-zero value out of this question 1.11 (and figure 1.33) in the Griffits Introduction to Eletrodynamics Book?

It all makes sense to me, but I don't know how to formalize it nicely. I wanted to divide it into two cases. First case where f is fixed in the segment. And a second case where f is not fixed in the segment. But I don't know how to prove it for the case where f i is not fixed

I am reading Manfred Stoll's book: Introduction to Real Analysis. I need help with Stoll's proof of Theorem 3.1.16 Stoll's statement of Theorem 3.1.16 and its proof reads as follows: Can someone please help me to demonstrate a formal and rigorous proof of the following:If $$U = X \cap O$$ for...

Could it be that the transformations keeping the wave equation invariant have other solutions than the usual Lorentz ones ?

Summary:: This question is about a Stokes' Theorem question that I saw on Khan Academy and I am trying to attempt to solve it a different way. The problem is as follows: Problem: Let \vec{F} = \begin{pmatrix} -y^2 \\ x \\ z^2 \end{pmatrix} . Evaluate \oint \vec F \cdot d \vec {r} over the...

I'm studying fluid and propulsion mechanics by myself. I stumbled upon this website from MIT: http://web.mit.edu/16.unified/www/SPRING/propulsion/UnifiedPropulsion2/UnifiedPropulsion2.htm#fallingblock It states that "Newton’s second law for a control volume of fixed mass" is $$\sum...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 5: The Riemann Integral and am currently focused on Section 5.2 Existence Results ... ... I need some help in understanding the proof of Theorem 5.12 ...Theorem 5.12 and its...

Hi everyone, I was wondering if it was possible to calculate a double integral by converting it to a line integral, using the greens theorem, and if so is it possible to get a non zero answer. if we were working on a rectangular region

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 5: The Riemann Integral and am currently focused on Section 5.2 Existence Results ... ... I need some help in understanding the proof of Theorem 5.12 ...Theorem 5.12 and its...

Noether's theorem tells us that an invariance of the Lagrangian yields a constant of motion. In this problem, that constant is: $$Q_v = p^a \Big( \frac{\partial q_a^{\lambda}}{\partial \lambda}\Big)_{\lambda = 0} + p^b \Big( \frac{\partial q_b^{\lambda}}{\partial \lambda}\Big)_{\lambda = 0}=...

The Poincare's recurrence theorem : This theorem implies the following: Suppose a container is divided in two by a wall. Half of it contains particles and the other none. If you were to remove the wall and wait a very very long time, the particles would eventually be found in the same half...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 5: The Riemann Integral and am currently focused on Section 5.1 Riemann Sums ... ... I need some help in understanding the proof of Theorem 5.10 ...Theorem 5.10 and its proof...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 5: The Riemann Integral and am currently focused on Section 5.1 Riemann Sums ... ... I need some help in understanding the proof of Theorem 5.10 ...Theorem 5.10 and its proof...

Hi All. Does anybody have a reference, (book, internet site) - besides those books of Paulo Ribenboim - where one can find a compilation of demonstrations of the Euclid's theorem on the infinitude of primes? As a suggestion, if the known proofs are neither too many not too long, it would be nice...

Hi all I was wondering if someone could help clear up some confusion about the Parallel Axis Theorem. I am trying to understand the purpose/benefit of applying the Parallel Axis Theorem with respect too the Second Moment Of Area. For example I have a beam that is under load. I have found its...

a) Proof: By theorem above, there exists a ##a \in \mathbb{R}## such that for all ##x \in I## we have ##f'(x) = a##. Let ##x, y \in I##. Then, by Mean Value Theorem, $$a = \frac{f(x) - f(y)}{x - y}$$ This can be rewritten as ##f(x) = ax - ay + f(y)##. Now, let ##g(y) = -ay + f(y)##. Then...

I just need the meaning of In.