In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect."In modern formal logic, the term is mainly used instead for a single proposition, often denoted by the falsum symbol

{\displaystyle \bot }
; a proposition is a contradiction if false can be derived from it, using the rules of the logic. It is a proposition that is unconditionally false (i.e., a self-contradictory proposition). This can be generalized to a collection of propositions, which is then said to "contain" a contradiction.

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27. ### I reconciling an apparent contradiction with thermostats and 24V

The attached photograph contains a diagram that represents my understanding of how thermostats are wired internally. I recently did six experiments with the low voltage wires in the air handler of my heat pump. Here are the results: Experiment 1# With the heat pump running in cool mode, R to Y...
28. ### I Is there a solution for the behavioural contradiction in RT?

In short: Consider a train-wagon with rest-length L, having a printer on the front and the rear that can put a dot on the rail. Both printers have synchronised clocks. The wagon, being the moving frame MF, has a speed v, and at t0 both printers simultaneously put a dot on the rail. Lsf is the...
29. ### I Why Does the Electric Field Calculation Diverge Inside the Volume?

Let: ##\nabla## denote dell operator with respect to field coordinate (origin) ##\nabla'## denote dell operator with respect to source coordinates The electric field at origin due to an electric dipole distribution in volume ##V## having boundary ##S## is: \begin{align} \int_V...
30. ### Use proof by contradiction to show there is no rational number such that....

Homework Statement Use proof by contradiction to show there is no rational number r for which r^3+r+1 = 0 Homework EquationsThe Attempt at a Solution Assume there is a rational number r for which r^3+r+1=0. Then r = (a/b) with a,b ∈ℤ and b ≠ 0, and a/b is in lowest terms Then a/b is a root...
31. ### Is my proof by contradiction valid?

Homework Statement If 3n+2 is odd, then n is odd Homework EquationsThe Attempt at a Solution assume 3n+2 is even, show n is odd 3n+2 = 2f => 3n+3 = 2f + 1 => 3(n+1) = 2f+1 so 3*(n+1) is odd form. Only odd*odd gives you another odd, so n+1 is odd. That means n is even. We have a...
32. ### B Base e to an imaginary exponent seeming contradiction

<Moderator's note: Moved from a homework forum.> 1. Homework Statement Given 0 < a < 1, i = √(-1), ei2πa = cos 2πa + i sin 2πa but also, ei2πa = (ei2π)a = 1a = 1 How to resolve the apparent contradiction?Homework Equations eab = (ea)b eix = cos x + i sin xThe Attempt at a Solution No clue...

I'm fairly sure that everything I wrote in the diagram in the attached photograph is consistent and accurate, but I don't understand how this can be. The rules involved seem to contradict each other. I hope you people can reconcile this for me. It's my understanding that in the diagram in the...
34. ### I Apparent Poynting vector contradiction

Hello all, Im trying to do a simulation of a poynting vector of an electromagnetic wave and I assume the following: At t=0 the E-field vector is (0,0,e^(-ikx)) and the H-field vector (0,e^(-ikx),0), hence orthogonal to it in vaccum, which is assumed, also the amplitudes are simplified both to...

Residential air-conditioners universally have a low voltage side and a high voltage side. The low voltage side of a residential air-conditioner is 24 volts. The high voltage side of a residential air-conditioner is 220/230/240 volts. I have heard several people say that a shock from the low...
36. ### B Is it Possible for a Short Circuit to Contradict Voltage in a Parallel Circuit?

Assume a superconducting parallel circuit being shorted, a 10V ideal battery, and a 5 Ohms resistor connected on one of its path. This means the shorted path has a 0 Ohm resistance, which also means it has no potential difference, how is this even possible if voltage across in a parallel circuit...
37. ### Contradiction in a charge redistribution problem

Homework Statement There are two metallic spheres, of same kind ,separeted from one another .One of them has charge 6 C wheras the another one is neutral.They are brought in contact for a long time.Then they are separeted again.Now what is the charges of the spheres?Homework Equations ...
38. ### B Special Relativity Self-Contradiction?

From his original thesis, Einstein said light speed is always constant (c). There is very clear evidence for this. Every ray of light moves in the “stationary coordinate system” with the same velocity c, the velocity being independent of the condition whether this ray of light is emitted by a...
39. ### I CMB results cause the contradiction of big bang theory

- The wavelength of light doesn't change at all in the galaxies because the space of the galaxies doesn't expand. - The wavelength of light should be different when it passes through the galaxy or not. However, this is contradictory to the observed result. So, the big bang theory is wrong.
40. ### Why Must n Equal 4q or 4q+2 If It Isn't 4q+1 or 4q+3?

Homework Statement For any integer n, let A(n) be the statement: “If n 2 = 4k + 1 for some k ∈ Z, then n = 4q + 1 or 4q + 3 for some q ∈ Z.” Use proof by contradiction to show that A(n) is true for all n ∈ Z.The Attempt at a Solution [/B] the answer sheet says that since n !=4q+1 and n !=...
41. ### Proof by Contradiction: Converse of A(n) Holds for All n ∈ Z

Homework Statement “If n = 3q + 1 or n = 3q + 2 for some q ∈ Z, then n 2 = 3t + 1 for some t ∈ Z.” Use proof by contradiction to show that the converse of A(n) is true for all n ∈ Z. For the proof by contradiction, on the answer sheet provided they have assumed n^2 = 3t+1 but n != 3q+1 and n...
42. ### My First Post: A Contradiction in Simple Free Fall?

Hello, Let us imagine a solid in a free fall on planet Earth and let us neglect the effect of air resistance on the motion of the solid. According to Newton's Second Law of Motion, since the only force being applied on the solid is its Weight, then its acceleration must be its Weight divided by...
43. ### Entropy Contradiction for a Single Harmonic Oscillator

Making use of the partition function, it is straight forward to show that the entropy of a single quantum harmonic oscillator is: $$\sigma_{1} = \frac{\hbar\omega/\tau}{\exp(\hbar\omega/\tau) - 1} - \log[1 - \exp(-\hbar\omega/\tau)]$$However, if we look at the partition function for a single...
44. ### Different answers from equation of continuity and Bernoulli

Hi there, So I was doing the dishes this morning using a sink wand hat can toggle between different flow speeds. The way that I've always thought of this working is using the equation of continuity: Volume flow rate: = Area*velocity Pressing a button on the wand decreases the cross-sectional...
45. ### Force exerted on the horizontal bottom of the container

Homework Statement In an empty container, having the shape of a Rectangular Parallelepiped, with width l=0.5m and MN=H=0.4m, and NP=L=0.75M. we poureda mass of mercury =2448kg. T0,T1,T2 have the same section which is 0.2 m^2. we give g=10N/kg, and density of mercury u=13.6 g/(cm^3)...
46. ### Apparent (clearly false) contradiction - Kepler's Third Law

Homework Statement When considering a satellite in geosynchronous orbit, its speed is zero across (relative to) Earth's surface. From Kepler's third Law: T2=(4π2r3)/(GM), we can derive that v2=GM/r This would tell us that as the radius of a satellite to Earth's centre increases, its velocity...
47. ### Ions passing through a parallel plate capacitor with a varying voltage

Consider the scenario Two parallel plates One ion particle (mass 1, charge +1) traveling parallel to the plates through the middle. Voltage of the plates is the same. As the ion travels between the plates the voltage on the plates ramps up, and the electric field between the plates remains...
48. ### Prove that 0.999.... = 1 is a contradiction

Homework Statement Prove that 0.999... = 1 is a contradiction Homework Equations None The Attempt at a Solution Assumptions : A. Let g(x) be a function of the form G(1) = 0.999^2 G(2) = 0.9999^2 Etc for all integer x > 0 B. 0.999... = 1 Argument: 1. G(1) ends in decimal 1 or 8 2. G(2)...
49. ### Proof by Contradiction: Showing a ≤ b when a ≤ b1 for every b1 > b

Homework Statement Let ##a,b \in \mathbb{R}##. Show if ##a \le b_1## for every ##b_1 > b##, then ##a \le b##. Homework EquationsThe Attempt at a Solution We will proceed by contradiction. Suppose that ##a \le b_1## for every ##b_1 > b##, and ##a > b##. Let ##b_1 = \frac{a+b}{2}##. We see that...
50. ### Computing angular speed wrt CM I get a contradiction

Hello! I have been brushing up my Rigid Body Dynamics. I tried computing the angular speed with respect the Center of Mass (CM) using the usual split of kinetic energy and also the split of Angular momentum using the CM. First, a simple case: Two particles of mass M each separated by a distance...