Contradiction Definition and 253 Threads

Homework Statement Imagine a particle tracing a counter-clockwise circular path on a flat table with a certain speed. The particle is tied with a massless string of length R to a point P at the center of the circular path. Will the particle rotate about P forever at constant speed in the...

I've been thinking about Magnetic Fields, and I think that I've found a contradiction in conventional physics theory. While comparing the Left-Hand-Rule for Motors (LHR) and the Right-Hand-Rule for Generators (RHR), I found this contradiction: The Left-Hand-Rule states that if the Magnetic...

If the abs(a+b) = abs(a) + abs(b), so the abs(z) = abs(x+iy) = abs(x) + abs(iy) = abs(x) + i abs(y). However, the correct wouldn't be abs(z) = √[x²+y²] ? √[x²+y²] ≠ abs(x) + i abs(y) => abs(z) ≠ abs(z) It's no make sense. What there is of wrong with those definions?

Homework Statement I'm trying to show that if ##a \approx 1##, then $$-1 \leq \frac{1-a}{a} \leq 1$$ I've started off trying a contradiction, i.e. suppose $$ \frac{|1-a|}{a} > 1$$ either i) $$\frac{1-a}{a} < -1$$ then multiply by a and add a to show $$1 < 0$$ which is clearly...

following is what little I know about energy:Energy: its the ability to do the work. First law says you cannot create nor destroy energy but can transform it to from one form to another. so its always 100 % conversation. but in a process you have 'work' done also. so does that mean 'work'...

Prove by contradiction that a real number that is less than every positive real number cannot be positive having troubles with this could someone give me a small hint to get started?

Homework Statement Hello Guys, can you check my proof. Problem statement: Let n be an integer such that n2 is even. Prove that n2 is divisible by 4. Proof by contradiction: Suppose n2 is not divisible by 4, thus n is odd. Such that n=2p+1, and n2=4p2+4p+1. Factoring out 2 we have...

According to my prof, increasing intensity of the light source in a photocell for the photoelectric effect does not increase the kinetic energy of photoelectrons emitted. Instead, the number of electrons emitted (and current) increases. Changing the colour of the light causes an increase in...

We know that the rate at which electrical work is done (electrical power) is defined as: P = I2*R , or: P = V2/R The formula P = V2/R implies that if the resistance of an electrical component (R) (for example, a light bulb) is decreased, the power consumption (P) will increase hence the...

Hi guys, let's say we have a wave where the power P is proportionate to the square of its amplitude, which is A^2. If now we have 2 identical waves in superposition in phase, then we have an amplitude of 2A am i right? Next, we realize that because of the amplitude of the superposed waves is...

2nd Order ODE "Contradiction"? To solve a 2nd order ODE, we can follow the steps as shown below. (Image 2 is a continuation from Image 1, apologies for the size difference.) :rolleyes: The method to obtain the solution is straightforward. Let's say \frac{d^2y}{dx^2}=ky If k = -1, a...

I am pretty confused in the following situation: Two identical clocks moving at a constant speed v from each other in x-direction. If each clock is made up of a ball moving at a constant speed of 1 on a ruler in y-direction, then the position of the ball of a clock is the time of the clock...

Hello I was doing an exercise that said: "If $P$ is a continuous operator in a Hilbert space $H$ and $P^2=P$ then the following five statements are equivalent". The first statement was that P is an orthogonal projection. Now this was suposed to be equivalent, under the condition of $P^2=P$, to...

Homework Statement The potential at a point is 20 V. Calculate the work done in bringing a charge of 0.5 C to this point. Homework Equations V = Ee / q W = -Ee The Attempt at a Solution Ee = 10 J W = -10 J But the answer is 10 J. Why isn't it negative? It's contradicting...

I was reading here https://www.physicsforums.com/library.php?do=view_item&itemid=294 gauss law's for magnetism says ∮B⋅dA = 0 but then faraday's law has d/dt ∮B⋅dA in it. Well if its 0 then d/dt of 0 is 0.

Homework Statement Please check that the proof is correct or not. Let ℝ+ = {x\inℝ: x>0} and T = {x\inℝ: 0<x<1}. Let x∈ℝ+ and t∈T Prove: If x\leq xt then x\leq 1. * You may assume any common properties of log(x) as well as : if 0<a\leq b then log(a) ≤ log(b) Any help is appreciated...

Homework Statement Prove that if x^2 + y = 13 and y \neq 4 , then x \neq 3 .Homework Equations N.A.The Attempt at a Solution The proof itself is simple enough: suppose x^2 + y = 13 and y \neq 4 . Suppose for the sake of contradiction that x = 3 . Then \begin{align*} (3)^2 + y &= 13...

So for the phase velocity of a massive particle we have Vph = Vg/2 for non-relativistic case Vph = c^2/Vg for the relativistic case Vg is the group velocity or particle velocity But there seems to be a contradiction in that for the non-relativistic case the phase velocity is...

Hi everyone, I'm a bit confused about the concept of the potential energy. Let's say we have the following scenarios here: https://dl.dropbox.com/u/29312856/Springs.jpg In the first scenario, we have two identical springs with spring constant 5000 N/cm angled at 20 degrees below the...

Is this how proof by condraction works? Say we want to prove A-> B. We prove by showing the statement 'A and not B' implies some statement C which is false (since it contradicts a known fact). Therefore, anything which implies C must itself be false, so 'A and not B' is false. I.e. A implies B.

I'm reading through a text's proof on proof by contradiction. But it makes inexplicable jumps and doesn't appear to use some of the things brought up. Here's the theorem and proof in the text (shortened with comment). \mbox{Theorem: If } \Sigma \cup \{\lnot P\} \vdash \{Q\} \mbox{ and...

Homework Statement Two equal, parallel and opposite forces at at both sides of a horizontal disk that lies on a smooth table, according to the picture. The mass is m and the moment of inertia is: kmR2 Angular momentum round the center point A: 2FR=kmR^2 \cdot \alpha. Angular momentum round...

The problem reads as follows: Let n be a positive integer that is not a perfect square. Prove that √n is irrational. I understand the basic outline that a proof would have. Assume √n is rational and use a proof by contradiction. We can set √n=p/q where p and q are integers with gcd(p,q)=1...

Homework Statement Prove that for any integer n n^2+n+1, can never be a square number. Homework Equations None. The Attempt at a Solution We could put the equation to a^2, (where a^2 is a square number) and solve for n and show that n can not be an integer. I tried quadratic...

Homework Statement Prove by Contradiction: For all integers x greater than 11, x equals the sum of two composite numbers. Homework Equations A composite number is any number that isn't prime To prove by contradiction implies that if you use a statement's as a negation, a contradiction...

Le Chatlier's Principle is used to determine the direction of a reaciton based upon a stress put on the system. In addition, Henry's law states that the solubility of a gas is related to the partial pressure of that gas. Therefore I present a seemingly contradictory setting: Example for...

Homework Statement Prove by Contradiction: For all Prime Numbers a, b, and c, a^2 + b^2 =/= c^2 Homework Equations Prime number is a number whose only factors are one and itself. Proof by contradiction means that you take a statement's negation as a starting point, and find a...

Say I have a statement like this: P implies (Q1 and Q2). If I wanted to prove this by contradiction, I would assume P and not(Q1 and Q2)=[(not Q1) or (not Q2)] both hold, and try to find a contradiction. My question is... Am I done if I find a contradiction while assuming P and [(not Q1)...

I came across this when doing another problem: Suppose we have 2 numbers, (a+b) and (c+d), which both equal 0. a+b=0 c+d=0 Then a+b=0=c+d, Thus, a+b=c+d However, a+b+c+d=0 Thus, a+b=-c-d Therefore, a+b=c+d AND a+b=-(c+d) How is this possible?

My textbook says that dE-TdS+PdV<0 for all irreversible processes. However, for reversible processes, the author says that dE-TdS+PdV = 0, and in fact this equation can be applied to irreversible processes because E is a state function. I'm confused -- this seems to be a contradiction.

I posted this in the number theory forum to no success... so I figured maybe the homework help people would have some input Let x,y,z be integers with no common divisor satisfying a specific condition, which boils down to 5|(x+y-z) and 2*5^{4}k=(x+y)(z-y)(z-x)((x+y)^2+(z-y)^2+(z-x)^2) or...

Let x,y,z be integers satisfying a specific condition, which boils down to 5|(x+y-z) and 2*5^{4}k=(x+y)(z-y)(z-x)((x+y)^2+(z-y)^2+(z-x)^2) or equivalently 5^{4}k=(x+y)(z-y)(z-x)((x+y-z)^2-xy+xz+yz) I want to show that GCD(x,y,z)≠1, starting with the assumption 5 dividing (x+y), (z-y), or...

It seems to me (though I would be *extremely* glad to be proven wrong here) that in mathematics we often blindly assume that the theorems we attempt to prove/disprove are either true or false. Such an assumption is implicit in every proof by contradiction. We eliminate the possibility of the...

I think the title is self-explanatory. The first theorem states that gravitational forces (1/r potentials in general) are able to produce stable orbits, whereas the second excludes stability! Can somebody help me to clear this out?

Homework Statement Suppose I want to prove the following statement by contradiction: P \longrightarrow (Q \land Z) Homework Equations If (Q \land Z) is false, then either: (i) Q is false and Z is true; (ii) Q is true and Z is false; (iii) Q and Z are false. The Attempt at a...

Hello I need help with a problem: If I see two identical charges moving in the same direction parallel to each other with the same constant velocity, my intuition tells me that the magnetic field generated by their movemente will cause them to attract much like what happensa with two wires with...

Suppose we have two objects and we're only talking about rectilinear motion. Initially, one object has mass m and is moving at velocity V. The other has mass M and is standing still. Then they hit each other and suppose that all kinetic energy is conserved and they stick together and move at...

My textbook (Halliday & Walker) explains that a charged conductor (a solid, of an arbitrary shape) in electrostatic equilibrium will have the electric field inside be 0 and all electrons will be on its surface. It proves this by saying that if the electric field inside was not 0, the free...

Continuity equation is dj+\partial_t\rho_t=0 where j and \rho are a time-dependent 2-form and a time-dependent 3-form on the 3-dimensional space M respectively. (see e.g. A gentle introduction to the foundations of classical electrodynamics (2.5)) If we use differential forms on the...

I never understand the proof by contradiction, because somewhere in the middle I always lost myself. In this https://www.physicsforums.com/showthread.php?t=523874 there's an example of proof by contradiction. We assume that if n^2 is odd than n is odd. This means that if n^2 is even, n...

Hi, I have a question about proofs by contradiction in general. Without getting into the mathematical details, suppose we had the statement: For every (condition A), B is true. If we want to prove this by contradiction, we want to assume the negation of this statement, and then prove it to...

Homework Statement If a,b and c are integers and a2+b2=c2, then at least one of a and b is even. [b]2. Contradiction statement There exist an integer a,b,c such that a2+b2=c2 and a or b is odd The Attempt at a Solution I am not sure if my contradiction statement is correct...

Hi all! We were given to proove or falsify the following statement: Given f(x)>0 \,\ ,\,x>0 \,\,\,\,,\lim_{x\to\infty}f(x)=0 Then f(x) is strictly decreasing at certain aεℝ for every x>a Now in their solution they contradicted the statement with: \newcommand{\twopartdef}[4] {...

list of contradictory situations. 1. Age of universe is determined by rate of proton decays at some place taking into consideration half life of proton. But since ALL protons were created after big bang, how can protons even decay. Considering the fact that their half life is greater than...

Now as you can see in the picture a common base configuration of BJT. The green markings in the picture are resistances. :p My question is: By KVL : VBB = VBE + IE*RB which means that IE is esentially a constant because VBB , VBE, RB are constants. Now If Voltage Vcb is increased Early...

Prove: If f approaches l near a and f approaches m near a, then l = m. ...Im skipping to the end of the proof... " to comlete the proof a particular ε>0 has to be choses for which the two conditions |f(x) - l|< ε and |f(x) - m|< ε cannot both hold if l=/=m." if l=/=m so that |l - m|> 0...

Homework Statement Prove that lim x→1 of x2 does not equal 1+10-10. You could use a proof by contradiction. (It is question 2.b here) Homework Equations δ-ε proofs! The Attempt at a Solution Given ε > 0, there is some number δ > 0 such that if: |x - a | < δ |x - 0 | < δ |x| < δ Then: |...

lim x->0 (sin x / x) =1...contradiction? sin(x)/x =1 (limit x to 0) this is an identity proved by using geometry and squeeze theorem ...right? now today i came across another question and doing it my way ...gives me two answers;) the question is limit x-->0 of [ x*sin(1/x)] my first...

Homework Statement The Attempt at a Solution I'm trying to show that Case 1 implies that \tau \in H, and since \tau was an arbitrarily chosen 3-cycle, then H must contain all 3-cycles, thus contradicting that H has 6 elements.

Hi, i didn't understand why we can't explain the situation simply as the cat is either dead or alive immediately after the poison was released or not, and not to assume that only when the observer opened the box the state of the cat was determined, what assumption does it contradict?