Contradiction Definition and 253 Threads

Q: S is a subset of the natural numbers (the counting numbers) with the following property n \in S \Rightarrow {1,...,n-1} \subset S. Prove, by Reductio Ad Absurdum, that S is equal to the set of all natural numbers.First of all, I want to make sure I got all the meanings of the symbols right...

Homework Statement Using contradiction, prove that for every four positive real numbers c, d, e and f, at least one of c, d, e, f is greater than or equal to the average of c, d, e, f. Homework Equations I don't believe that there are any relevant equations for this problem. I do know that...

Proving the "proof by contradiction" method This can get a little bit fundamental or "axiomatic", if you will. Let's say we can describe sets by prescribing a fixed property P on objects of a certain type, and claiming that a set is a collection of objects satisfying P; i.e. A = \{x : P(x)\}...

Homework Statement Just as the title said, I need to prove: For any integer n, n2 - 2 is not divisible by 4 by the method of proof by contradiction. Homework Equations (Relevant by division into cases) Even numbers = 2k for some integer k Odd numbers = 2m+1 for some integer m...

yz = ln(x+z) So I'm trying to find the tangent plane to the surface at a particular point (x0,y0,z0). Here's the general formula: Fx(x0,y0,z0)(x-x0) + Fy(x0,y0,z0)(y-y0) + Fz(x0,y0,z0)(z-z0) = 0, where Fx, Fy, and Fz are the partial derivatives of the below F(x,y,z): 1. F(x,y,z) = ln(x+z)...

When you learn about phase diagrams of pure substances, you learn that the liquid and gas phases are in equilibrium only along the line separating the pure liquid and pure gas regions. But if you have a sample of liquid in a closed container with some empty space in it, that empty space...

i just started studying quantum mechanics in my college...i asked a number of teachers and seniors that why psi(ψ) is maximum at r=0, also (ψ)^2 is maximum at r=0 but probability is maximum at r= a(knot) for 1s orbital this seems a contradiction to me that on one side we are ssaying ψ is...

I am currently studying surface tension. I came across a topic named "capillarity" where it is said that mercury falls down in capillary tube. But it rises in a barometer . Why is it so?

I recently studied that equilibrium constant is independent of concentration. But if you multiply both sides of equation by any number, equilibrium constant changes. Isn't this contradictory?

Homework Statement Two Questions: 1. Prove, by contradiction, that if a and b are integers and b is odd,, then -1 is not a root of f(x)= ax^2+bx+a. 2. Prove, by contradiction, that there are infinitely many primes as follows. Assume that there only finite primes. Let P be the largest...

So "A shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shell’s charge were concentrated at the center of the shell" and also, "If a charged particle is located inside a shell of uniform charge, there is no electrostatic force on the particle...

The second law of thermodynamics states that the entropy in a system, such as our universe, always increases. The third law, however, says that entropy reaches zero as a system approaches absolute zero temperature. Our universe has been cooling off since its origin (because of its...

Hello. Galois theory tell us $x^5-6x+3$ is not solvable by radical but every equation lower than fifth can solve by radical. If $G$ is solvable and $H$ is solvable too $G*H$ are solvable. For $x^5-6x+3$ we can use Newton’s method and find one root of this equation. We obtain $x=1.4$ and...

Homework Statement I have to design an experiment where I am supposed to project an object horizontally from some point above ground level, measure the distances, calculate the average horizontal distance dx, then use that to calculate the initial and final velocities yatta yatta. Anyway I made...

Sometimes I find that while a proof can be carried out "by contradiction", this is a pretty sloppy way of proving the desired statement. I wonder if the "←" direction of the following proof is sound presentation of proof by contradiction. Statement. An integer is even if and only if its square...

Homework Statement A Yo-Yo of mass M has an axle of radius b and a spool of radius R. Its moment of inertia can be taken to be MR2/2. The Yo-Yo is placed upright on a table and the string is pulled with a horizontal force F as shown. The coefficient of friction between the Yo-Yo and the...

Homework Statement A large cylinder is filled with an equal volume of two immiscible fluids. A balloon is submerged in the first fluid; the gauge pressure in the balloon at the deepest point in the first fluid is found to be 3 atm. Next, the balloon is lowered all the way to the bottom of the...

A simple electric circuit (such as one composed of a battery with Emf V and resistor with resistance R) is in an electrodynamic state since the battery's potential difference creates an electric field in the circuit's wires, which in turn moves charges around. So potential difference in wires is...

The universe is said to be 13.7 Billion years (http://en.wikipedia.org/wiki/Age_of_the_universe" . So, for the present galaxy UDFj-39546284 and the present Earth to have traveled as far as they are now, and even if we assume that the big bang occurred right between Earth and UDFj-39546284, it...

We all know that the universe is expanding and for that matter accelerating. Science is now starting to realize that the universe will expand forever and the big crunch will never occur due to recent data of a supernova. My point to all this is, quantum theory states that a vacuum must always...

So if I want to prove. A=>B for all x. Does the following work? Suppose for contradiction, B is not true for all x, that is, there exists at least one x such that B is not true. In particular, assume that B is true for x=c and B isn't true for all other x. If I arrive at a...

Homework Statement "Prove that when an irrational number is divided by a nonzero rational number, the resulting number is irrational" The Attempt at a Solution By contradiction: Prove that when an irrational number is divided by a nonzero rational number, the resulting number is...

Please Help! proofs using contrapositive or contradiction Homework Statement Prove using contrapositive or contradiction: For all r,s∈R,if r and s are positive,then √r+ √s≠ √(r+s)

Limit definition gives a contradiction! say we are given sequences a(n), b(n) such that, a(n)->a, b(n)->b that means for epsilon>0, a-epsilon<a(n)<a+epsilon when n>N1 b-epsilon<b(n)<b+epsilon when n>N2 set N=max(N1,N2) when n>N...

let's say a train is traveling at relativistic speed along a straight line to right, and a man is standing in the middle of the train. Both end of the train was installed a gun which aims at the man. The right-ward gun aims at the man's leg and the left-ward gun aims at the man's head. In...

suppose we have a point charge q near the grounded conducting sphere. we know that the work down by electric field of the sphere for taking the point charge from surface of the sphere to infinite is infinit. but the potential energy in the grounded surface and infinite is zero. what is the reson...

we know that the electric field between the planes of planar capacitor is σ/ε (according to gauss law) however we have two conducting plate that each plate produe this electric field that are in the same direction therefore we must have E=2σ/ε what is the reason for this contradiction.

Homework Statement Ok so (1) E = hf and (2) lambda = h/p Homework Equations The Attempt at a Solution For a particle mass m, speed v, momentum p Surely if p^2 / 2m = Ek (kinetic energy) then we can write from (2) Ek = h^2/ 2m lambda^2 But from (1) we can write E =...

In section 1.2 of Taylor and Wheeler's Spacetime Physics, a rocket moves past a laboratory (on Earth). Attached to the rocket is a pin. From that pin a spark is emitted at two locations in the lab, separated by 2 meters. The observer in the rocket measures the elapsed time between the sparks, as...

In figure 3-1 (page 63) of Taylor and Wheeler's Spacetime Physics, the observer on the train determines that the lightning strikes are not simultaneous because the flashes do not reach her simultaneously. I see two problems with this. 1. The narrative in figure 3-1 contradicts the text in...

Homework Statement I want to practice proofs by contradiction I am trying to prove that sin(x)=b has infinite distinct solutions in R for every b in [-1,1] Homework Equations The Attempt at a Solution assume it has finite amount of solutions called set Z let k be in real number...

Do these two answers contradict each other: Q1) Four students are discussing a circuit. The circuit is in series and contains a lamp, an ammeter and a 10V battery. Andy: the current in the lamp consists of negative charges moving from the negative batter terminal towards the positive...

Homework Statement A metre scale made of steel is calibrated at 20 degrees Celsius to give correct reading. Find the distance between 50cm mark and 51cm mark if the scale is used at 10 degrees Celsius. Coefficient of linear expansion of steel is 1.1 x 10-5 C-1 Homework Equations...

Hi, Second time I'm writing this question, the first one seems to have been lost in cyberspace but sorry if it somehow comes back and appears twice. Anyway, you know how kinetic energy depends on velocity, so that the energy of a particle collision will be different for two frames of...

Homework Statement (1 2 3 4 5) (2 1 3 5 4) Write the bottom number as a product of transpositions Homework Equations The Attempt at a Solution 41352 41325 41235 42135 42315 24315 24351 21354 (2 4) (2 5) (2 3) (2 1)...

A thought experiment: Say that you and I decide we are going to go into orbit around a black hole. I am brave and you are weak, so I decide I'm going to take the plunge and you just stay in orbit. As I fall toward the black hole, the strength of the gravitational field increases, and time for...

Homework Statement Wrie out the truth table for the statement form P -> ~(Q ^ ~P). Is it a tautology or a contradiction? Homework Equations The Attempt at a Solution First off is it true to say that P -> ~(Q ^ ~P) and P -> (~Q v P) are equal. P | Q | ~P | ~Q | P -> (~Q v P)...

Homework Statement If f(x) <= g(x) then lim[x->a] f(x) <= lim[x->a] g(x) provided that both of these limits exist. 2. The attempt at a solution I've been able to prove it by contradiction. So I assumed that l = lim[x->a] f(x) > lim[x->a] g(x) = m. Therefore, l - m > 0 and I could...

Is square root a function in this way? f:\mathbb C\rightarrow\mathbb R^+ However contradiction can be drawn:\sqrt{x^2}=|x|\text{ and } i^2=-1 \sqrt{-1}=\sqrt{i^2}=|i|=1 \sqrt{-1}=1 ??What is the problem in the...

Homework Statement Prove or disprove the statement: 13 + 2√6 is an irrational number Given that √6 is irrational Homework Equations Rational number = p/q where p and q are integers The Attempt at a Solution Assume that 13 + 2√6 is a rational number Rational number =...

Okay, the title is promising something big. I'm sorry, it's probably not big, but it does seem important, although for some it will be unsignificant, I suppose it depends on your interests in physics: So if you have an infinite plane with current density J (current per meter width) (say...

Hi In superconductors, the fermions are interacting. In order to diagonalize our Hamiltonian (which contains the product of four fermion operators), we use Wick's theorem to approximate the product of four fermion operators by the product of two fermion operators. Now, a Hamiltonian...

Hi, everyone: I am confused about the result that every map from a contractible space X into any topological space Y is contractible. I think the caveat here is that the homotopy between any f:X-->Y and c:X-->Y with c(X)={pt.} is that the homotopy is free, i.e., the...

I am studying differential equations from this book by Edwards and Penney, and I seem to have stumbled on this rather bizarre contradiction which I can't seem to get myself out of. The problem, which is a variation on the classic rope falling off a table, goes as follows: "Suppose that a...

In physics the moment of inertia of a thin rod which rotates around an axis through its center of mass is : I cen = 1/12 m L sq (1) Where: m is the mass of the rod, L is the length of the rod. The moment of inertia of a thin rod which...

http://i49.tinypic.com/1yu634.jpg this is a part of the solution " the is a voltage drop on capacitor C1 which makes current shock on C1 and a current shock on R2 and R3 and it makes a KVL contradiction on the right branch and the outer branch. and that's why the continuety laws...

Contradiction in the equations of motion...??! I' ve found a strange contradiction between the fist and second equations of motion. First we start with the second equation: s = ut + 1/2at2 We factor 't' out, whoch gives us: s = t(u + 1/2at) We divide both sides by 't', and on...

This is a question with regard to a specific step in a problem. I don't think it is necessary to elaborate the whole problem. Homework Statement Resolve this apparent contradiction. I get two different answers for Na|n\rangle Homework Equations For a fermionic oscillator, we have...

In quantum mechanics, the phase velocity is f/k=E/p because of E=hf and p=hk where k=1/wavelength. In special relativity, E=mc^2 and p=mV (V<c). So, E/p=cc/V >c. To photons in media, however, the phase velocity is f/k =c/n<c. What’s wrong ?

Hello everyone! I apologize if my first post is of a problem that may seem like a really silly one. But it was something we were stuck with today in Modern Physics class. It is NOT a homework assignment! We have proved that relativistic force, F = m*(du/dt)*(gamma)3 where gamma is the Lorentz...