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.
The formula for motional EMF is
$$\oint({\bf{v}}\times{\bf{B}})d{\bf{l}}=-\frac{d}{dt}\int{{\bf{B}}\cdot{\bf{\hat{n}}}da}$$However applying this for a rotating disk of radius a there seems to be a sign contradiction
$${\bf{v}}\times{\bf{B}}=\omega s{\bf{\hat{\varphi}}}\times...
There is a proof that shows by induction (and by contradiction) that the identity permutation decomposes into an even number of transpositions. The proof is presented in the first comment here...
As a transformer freq bet higher, inside induction get more efficient i.e. less loss:
1. Hysteresis loss = η * Bmax^n * f * V.
2. Eddy current loss( proportional to B2mf2Bm2f2 )Now it seems that losses increases with increase in efficiency...
But the above equations are valid when max flux...
This is more a general question that this problem spurred and this is what I came up with. I do not feel it is acceptable but would like clarification moving forward.
My text states the format for proof by contradiction is as follow;
Proposition: P
PF: Suppose ~P.
...a little math and...
Hope this question can be quickly clarified:
There was a statement that the General Relativity can be interpreted by speaking of an ether whose state varies from point to point. Is this correct?!
This one brought a smile to my face:
COWS All the Way Down.
I'm not sure whether this is astrology, climatology or down right nonsense, but I hope it gives you a smiley pause too.
According to equation (2.33) divergence of the Poynting vector or the outflow of electromagnetic power is equal to the stored magnetic field, stored electric field and ohmic losses.
My contradiction is the following:
Inside a steady state DC current carrying wire, there will presumably be a...
Homework Statement:: Why is the entropy of a closed system constant in a reversible process, and not related by ##\Delta S = \int_{i}^{f}\frac{dQ}{T}## (See below for the question in more details)
Relevant Equations:: ##\Delta S = \int_{i}^{f}\frac{dQ}{T}##
I am reading chapter 24 of Physics...
I found an interesting math result ("halting problem is essentially solvable") yesterday, but now I see a contradiction (it follows "halting problem is solvable"). Participate in finding my error.
Here is my short yesterday article (with links to other yesterday articles):
[Unacceptable...
Dear Everyone,
I am attempting a proof of contradiction for this problem. I am stuck on next step.
My attempt:
Assume that ##S## is bounded. Choose a ##N=\text{greatest integer function of} R+1##...
Here is where I am stuck. I want to show that the sequence is moving away from the closed ball...
Proof by contradiction (for some reason the LaTeX code is not working for me. Sorry)
Lets assume that A, B, and C are non-zero real numbers; A = B ; and C is not equal to 1.
A/ B = C
A = B x C
But BxC could be equal to B, if and only if C =1
Also, could you recommend a book where I...
I started reading about the “relational” interpretation of QM (RQM). I’m stuck on what appears to be a contradiction. The simplest way I can think to explain it is with a slight complication added to the Wigner’s friend experiment, adding an extra operation after the friend F measures the...
Ok I am trying to brush up my real analysis skills so that I can study some topology and measure theory at some point.
I found this theorem in my notes, that is proven by using proof by contradiction. However, I have a hard time understanding what the contradiction really is...
Here is the...
So, i was trying to calculate, the net force between 2 point charges in their rest frame, and in a frame where they are moving.
So, assume, there are 2 point charges each of charge +q.
They are r distance apart from each other and moving parallel to each other with a speed v relative to a lab...
I find the following definition in my complex analysis book :
Definition : ## F(z)## is said to be a branch of a multiple-valued function ##f(z)## in a domain ##D## if ##F(z)## is single-valued and continuous in ##D## and has the property that, for each ##z## in ##D##, the value ##F(z)## is one...
I get a nonsensical result. I am unable to understand where I go wrong.
Let's consider a material with a temperature independent Seebeck coefficient, thermal conductivity and electrochemical potential to keep things simple. Let's assume that this material is sandwiched between 2 other materials...
When conversing informally about QM, there is often wonder about the apparently acausal nature of processes that we may call "quantum leaps" between physical states. It is often said that the purely mathematical foundations of QM give no reason for such wonderment, i.e., that the math, in...
While studying the fundamentals of sound waves in organ pipe, I noted that the fact about phase of reflected waves is contradicting while referring multiple sources
This book of mine describes the reflection from a rigid surface/closed end to be in phase
Whereas this one describes the...
In b). Since the force T is perpendicular to the trajectory of the mass m, T does not perform any work on m, therefore the translational mechanical energy is conserved, from which I deduce that the initial speed is equal to the final speed, moreover, the speed is constant.
Now, when analyzing...
Normally you can do reduction formula type questions with I.B.P., but here that just results in something like $$I_n = \left[-f(x) \cos{x}\right]_0^{\pi} + \frac{q^n n}{n!} \int_0^{\pi} \cos{(x)} x^{n-1} (\pi - x)^{n-1} (\pi - 2x) dx$$I can't seem to get anywhere from here though. Substitutions...
If we have a conservative vector field, then we can describe it as ##\textbf{F}=\nabla\phi## where ##\phi## is some potential.
This here is the derivation of Newtons law of gravity:
Where ##\nabla u## is the gravitational potential. If we were to ignore it as a gravitational field, why is it...
1905 paper, looks to me like:
Postulates:
- principle of relativity
- definite velocity of c
Definition of inertial frame coordinate system
- using rigid rods to identify position of A at rest WRT to the IFR coordinates
Seems clear that rigid rods may be used to identify the place of other...
I have reached a conclusion that no such z can be found. Are there any flaws in my argument? Or are there cases that aren't covered in this?
Attempt
##\log(\frac{1}{z})=\ln\frac{1}{|z|}+i\arg(\frac{1}{z})##
##-\log(z)=-\ln|z|-i\arg(z)##
For the real part...
This video here <link deleted> 8.50 to 9.50 minutes , shows an apparent contradiction in time dilation, in the "twins paradox" the clock that is accelerated is relative, i.e. from Earth the spaceship moves but from the spaceship the Earth moves. I know time dilation is a real thing used in real...
(Black one is the object and grey is its image.)
We know from Snell's Law:
$$
n_1\sin\alpha=n_2\sin\theta
$$
And I have been said that:
$$
a=b\ (1)\\\ and\\\ \frac{h}{h'}=\frac{n_2}{n_1} \ (2)
$$
Let's begin.
$$...
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...
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...
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...
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...
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...
<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...
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...
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...
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 ...
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...
- 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.
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 !=...
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...
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...
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...
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...
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)...
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...
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...
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)...
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...
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...