Contradiction Definition and 259 Threads

Hello! (Wave) Let $(a_n)$ be a sequence that satisfies the relations $a_{n+1}=\frac{a}{a_n}$, where $a>1$, and $a_0<1$. I want to show that the sequence does not converge. I have thought to suppose that the sequence does converge. Then $a_n \to l<+\infty$. Then we get that $l=\frac{a}{l}...

I was reading Einstein's book on Relativity. He says something about a contradiction between the law of Propagation of light in vacuum and the principle of relativity(which he calls in restricted sense).What is this contradiction?How does it lead to Einstein's conclusion that time and distance...

Say I have the theorem ##p \rightarrow q##. What is the difference between proving that ##\neg q \rightarrow \neg p## is true and showing that ##\neg (p \rightarrow q) = \neg p \wedge q## leads to a contradiction?

I don't understand why LzL+ acting over m is Planck constant(m+1) L+|m>. I 've done it and I've got to a contradiction. Am I doing something wrong?

An absolute value property is $$\lvert a \rvert \geq b \iff a\leq-b \quad \text{ or } \quad a\geq b,$$ for ##b>0##. Is this true for the case ##a=0##? I mean if ##a=0, \lvert a \rvert =0## so ##0 \geq b##. But ##b## is supposed to be ##b>0##, so we have a contradiction. How can this property...

Hello all, I have a question that's been bothering me the last few days and wasn't sure where to turn. Recall the original Special Relativity thought experiment: A spaceship travels at constant velocity v, moving in the positive x direction. An observer on the spaceship emits a photon directly...

Hello everyone, I am working on understanding how Kirchhoff's Radiation Law applies in the real world. Basically, the absorbed solar radiation must equal the thermal radiation if a surface is to be at equilibrium. Certain relationships follow from this assumption, namely, for an opaque...

in an attempt to get a better understanding of what happens during a measurement i have constructed a gedanken-experiment with two photon interference that regardless of its outcome seems to contradict quantum mechanics in one way or another and i was hoping to get a clarification here where i...

In Chapter 11, section 11-4, subsection friction and rolling, it is stated that the static frictional force is along the same direction as the direction of motion because the point of contact of the wheel with the floor is moving in the opposite direction. Then, in the next subsection, the same...

I need to understand something about proof by contradiction. Suppose there is an expression "a" and it is known to be equal to expression "b". Furthermore, suppose it is conjectured that expression "c" is also equal to expression "a". This would imply expression "c" is equal to expression...

Hello. I'm currently studying about natural numbers and I encountered the theorem of definition by recursion: This states: Let ##H## be a set, let ##e \in H## and let ##k: H \rightarrow H## be a function. Then there is a unique function ##f: \mathbb{N} \rightarrow H## such that ##f(1) = e##...

This is a linear algebra question which I am confused. 1. Homework Statement Prove that "if the union of two subspaces of ##V## is a subspace of ##V##, then one of the subspaces is contained in the other". The Attempt at a Solution Suppose ##U##, ##W## are subspaces of ##V##. ##U \cup W##...

Proof by contradiction starts by supposing a statement, and then shows the contradiction. 1. Homework Statement Now, there is a statement ##A##. Suppose ##A## is false. It leads to contradiction. So ##A## is true. My question: There are two statements ##A## and ##B##. Suppose ##A## is true...

Imagine there is a frictionless disk that spins with angular speed w. There is a ball on it that sits motionless at some radius r from the center. Now, switch to the frame of the rotating disk. In this frame the ball should be spinning with speed w * r. Edit: To be clear, the ball is NOT moving...

Say I have an exothermic reaction, whose change in Entropy is positive. (not the most common of reactions, but it can still happen) If I increase the temperature, by La Chatlier's principle, the reaction should move to the left. However, by Gibbs free energy, if I increase the temperature, the...

Assuming you've sufficiently proven your inductive basis, can you complete a proof by induction in the following manner: Make the inductive hypothesis, assume P(n) is true for some n. Assume P(n+1) is not true. If it follows from the assumption that P(n+1) is false that P(n) must also...

In my thread titled "What does cold hydrogen gas emit at 1420 MHz?", physicsforums member blueleaf77 told me the following: "There are three main types of interaction between bound state electrons and photons: absorption, stimulated emission, and spontaneous emission. The first one involves...

In the process of doing a proof by induction, can you use a contradiction to show that if P(k) holds then P(k+1) must hold? What I mean is, after establishing that P(0) holds, can I assume that P(k) holds and that P(k+1) does not, and show that a contradiction arises, and thus conclude that if...

Homework Statement Prove by contradiction that if b is an integer such that b does not divide k for every natural number k, then b=0. Homework EquationsThe Attempt at a Solution I know that proof by contradiction begins by assuming the false statement: If b is an integer such that b does not...

I have been unable to find a satisfactory explanation of this problem, elsewhere. Consider an uniform electric field, E, along the y axis. Consider also a uniform magnetic field, B, along the z axis. If we release a particle (charge=q, mass=m) at rest on the origin at time t=0, what will be...

Hey! :o I want to show that $A_4$ has no subgroup of order $6$. $A_4$ is the group of even permutations of $S_4$. Suppose that $A_4$ has a subgroup of order $6$. Could you give me some hints how we could get a contradiction? (Wondering)

1. Surfactant molecule is made from water-loving head and grease-loving tail (Figure 1). http://tinypic.com/r/2j2gdah/9 (Figure 1) My question: How do we measure the cross-sectional area of the alkyl chain of surfactant? Do we measure it vertically (refer to GREEN DOUBLE ARROWS of Figure 1) or...

The following equation (5.122) is the minimum-uncertainty wave function, which is a Gaussian wave packet. Since it is Gaussian in ##x##, we may get ##\Delta x## directly from the ##\sigma## of the Gaussian distribution: ##(\Delta x)^2=\frac{\hbar^2}{2(\Delta p_x)^2}##. We have ##\Delta x\Delta...

I have had some criticism on a post of mine in another topic. Since I don't want to pollute that thread with my own discussion, and since I am a layman and am really curious about the answer, I'll pose my question here. Consider two polarisation-entangled photons A and B measured by Alice and...

Hi all, I'm considering an fluids example that's giving me an apparent contradiction when I consider it from the perspective of Bernoulli's Equation vs. the Equation of Continuity. What I'm thinking of is the common observation that putting one's thumb over a garden hose results in an increase...

For prime numbers, $a$, $b$, $c$, $a^2 + b^2 \ne c^2$. Prove this by contradiction. So, I get that $a^2 = c^2 - b^2 = (c - b)(c +b)$ And I get that prime numbers are the product of 2 numbers that are either greater than one, or less than the prime numbers. But I'm unsure how to go from here.

Homework Statement Problem 1 Assuming that the people in D and C all have KTP (Citizen ID in my country) IDs, let: D = {x |x is the KTP ID of a student in your Basic Calculus class}, C = {y |y is the KTP ID of the biological father/mother of a student in your Basic Calculus class}, and f : D...

We know that the rotational inertia I of a certain object is I =∫r∧2 dm where r is the distance between the axis of rotation and the increment of this object that carries a mass dm. What confuses here is the following: Take for example a hoop of mass M and radius R. Integration theory gives...

Homework Statement Using the method of contradiction prove the following. There's no real number x such that |x-2|+|x-3|=1/2 Homework EquationsThe Attempt at a Solution I can see that the least possible value that LHS can take is 1. That is when x=2.5 which is the middle value of 2 and 3...

Homework Statement Prove the following identity \nabla (\vec{F}\cdot \vec{G}) = (\vec{F}\cdot \nabla)\vec{G} + (\vec{G}\cdot \nabla)\vec{F} + \vec{F} \times (\nabla \times \vec{G}) + \vec{G}\times (\nabla \times \vec{F}) Homework Equations vector triple product \vec{a} \times (\vec{b}...

Homework Statement Suppose that a and b are nonzero real numbers. Prove that if a< 1/a < b < 1/b then a<-1. Homework Equations Givens: a and b are nonzero real numbers, a< 1/a < b < 1/b, and a≥-1. Goal: Arrive at a contradiction.The Attempt at a Solution Scratch work: First establish whether...

TERMS: Slip Plane: is the plane that has the densest atomic packing—that is, has the greatest planar density. Slip Direction: corresponds to the direction in this plane that is most closely packed with atoms—that is, has the highest linear density. NOMENCLATURE: θ = angle of the slip plane as...

I've been using euler's formula now more than I have in the past, (using it for circuit analysis stuff), and so its been floating around in my head a bit more. Say you have e^{2πi}=1 and you take the natural log of both sides. \log_e( e^{2πi})=\log_e(1) 2πi=0 uhhhhh... :confused:

How can I derive a contradiction from the following nasty statement: Assume $\sqrt{5} = a + b\sqrt[4]{2} + c\sqrt[4]{4} + d\sqrt[4]{8},$ with $a,b,c,d \in \mathbb{Q}$? *This is the last piece of an effort to prove that the polynomial $x^4-2$ is irreducible over $\mathbb{Q}(\sqrt{5}).$*

Let S be the frame where the Sun is at rest. Imagine light from the North Star reaches the centre of the Sun, and let's define the equatorial plane as the plane that is perpendicular to this light and cuts the Sun into two hemisphere. Suppose a distant star A is on this equatorial plane and its...

Suppose frame ##S^\prime## moves in the positive ##x## direction at ##v## with respect to frame ##S##, and frame ##S^"## moves in the positive ##y## direction at ##v^\prime## with respect to frame ##S^\prime##. Then, ##E^\prime_x=E_x## ##E^\prime_y=\gamma(E_y - vB_z)## ##E^\prime_z=\gamma(E_z...

Homework Statement lets say i have an int n that is greater than 2. I know n!-1 = xk where x and k are integers I must show that x <= n leads to a contradiction The Attempt at a Solution i assume x = n n!-1 =nk (n-1)! -1/n = k it seems to me that because of the 1/n k would not be an integer...

Consider an ideal gas operating in a quasi-static (very slow) cycle that is identical to the heat engine version of the carnot cycle in every aspect, except that friction is present. So even though the cycle is quasi-static, it is irreversible due to friction. Now the question is: How does the...

Consider a gas as your system, confined in the usual frictionless piston-cylinder. The piston is massless, external pressure is constant, Pext. Let the system be at initial state T1 and P1 = Pext. We want to compare the following two processes: in the first process, we reversibly heat the gas...

Hello again. I recently submitted a thread asking for feedback on a couple of very basic proofs for an exercise from the book "How To Prove It" by Velleman. This is another request for you to help me understand how wrong my proof for a new exercise could be improved. 1. Homework Statement...

0. Background First and foremost, this is a proof-reading request. I'm going through Velleman's "How To Prove It" because I found that writing and understanding proofs is a prerequisite to serious study of mathematics that I did not meet. Unfortunately, the book is very light on answers to its...

I've worked with Euler's Identity for physics applications quite a few times, but ran into a "proof" of a contradiction in it, which I can't seem to find a flaw in (the only time I've ever had to do any proofs was in high school). I've derived Euler's equation in two different ways in past...

Hey guys, This is my fist post and I am curious enough about this to get a new account. Go on wikipedia for the formula and derivation of the abraham lorentz force: http://en.wikipedia.org/wiki/Abraham%E2%80%93Lorentz_force Anyway my question is as follows: Lets consider a charge that I am...

I was studying the first chapter "Sets and Structures" of the "A Course in Advanced Calculus - Robert S. Borden". I faced a difficulty at the part of the proof of contradiction. I got confused at what this B= \{x \in A : x \not\in f(x) \} is and how it's true that If~y \in A ~\text{is such...

We read that the a couple is a free vector, i.e it does not depend on the point of application. However, please consider the following example: If you apply two equal magnitude forces anti-parallel to each other, one on each side of the wheel, a couple is formed, and so the wheel will rotate...

Hi, dear forum members! It is well known, that if one makes the current carrying wire more thicker, for example 3 times, that means the current goes up also 3 times. Microscopically that seems plausible, because, when we consider that a cross section is made of atoms, then it is apparent, that...

Problem: Attempt: But here is what happens when I apply nodal analysis to the same node at t>0: Is this a contradiction? Is the voltage of the resistor at t=0+ equal to 16V or 0V?

It's not really homework, it's something we did in class, but I don't understand why we did it this way. Problem, you have a cylinder with uniform charge density rho and some point p which lies on the x-axis (i'll draw a picture). Find the potential at p. Solution. You have to...

I'm reading a book about unification of general relativity and quantum physics. The author states that one of the axioms of GR is background-independence, meaning that space-time has no external reference points. All distances and motions in space-time are relative. On the other hand, the...

There seems to be two concepts of what constitutes a "meaningful" proposition in logic: one is that you can build up the proposition via the syntactical rules. However, another approach is to say that a meaningful sentence is that it is assigned a set in a model (even if it's only the empty...