Argument Definition and 388 Threads

Find the error in the following argument by providing a counterexample. “The reflexive property is redundant in the axioms for an equivalence relation. If x ∼ y, then y ∼ x by the symmetric property. Using the transitive property, we can deduce that x ∼ x.”

In order to construct a geometric series we do the following: chose a number a such that a does not equal 0 and a second number r that is between (-1,1). We call r the ration because it is the ratio, the progression of each term to its predecessor. We have An=a+ar+ar^2+ar^3...ar^n We multiply...

How can I find an Integral of an exponential with Polynomial argument with finite limits: \int_0^\pi \exp^{-a x^2 -b x^4} dx \\ \int_0^\pi \exp^{-a x^2 -b x^4} (x - x^3)dx

In Celestial Mechanics the equation: LP = w + N (Longitude of the Perihelion = Argument of the Perihelion + Longitude of the Ascending Node) is confusing. Both "LP" and "N" are on the Ecliptic Plane but "w" is not. "w" is on the Elliptic Plane with a tilt of "i" Inclination from the Ecliptic...

I have the sum, $$\sum_{n=1}^{\infty} \frac{1}{n^{3}}\sin(n \pi x) \text{, where }0 \leq x \leq 1$$ I have to show that the series converges, so I'm going to use the Comparison Test. $$ \text{If }0 \leq a_n \leq b_n \text{ then}$$$$\text{If }\sum b_n \text{ converges then }\sum a_n \text{ must...

Homework Statement For the function ##V(f) = A \tau sinc(f \tau)## in the picture how do you conclude that the argument of ##V(f)## is 0º, +180º or -180º? Homework Equations ##arg = arctan({\frac{Im}{Re}})## The Attempt at a Solution The upper graphic represents the absolute value of the...

I am working on proving that an equilibrium point of a two-dimensional dynamical system is globally asymptotically stable. The background and justifications are below. I have gotten to the final steps (in bold), but cannot justify it. It seems right intuitively. Can someone navigate the argument...

A hole in the LHC's vacuum bubble safety argument One of the four specific risks considered in the most recent official safety review for the Large Hadron Collider (LHC) is the possibility that LHC collisions could trigger a transition to a lower-energy vacuum state. The current review by the...

Homework Statement In each case, state whether the assertion is true or false, and justify your answer with a proof or counterexample. (a) Let ##f## be holomorphic on an open connected set ##O\subseteq \mathcal{C}##. Let ##a\in O##. Let ##\{z_k\}## and ##\{\zeta_k\}## be two sequences...

Let us assume that an observer is stationary at the origin in expanding space. We assume the FRW metric near the origin is given by: $$ds^2=-dt^2+a(t)^2dr^2$$ Let us assume that the observer measures time by bouncing a light beam at a mirror that is at a constant proper unit distance away from...

Brocard's problem is a problem in mathematics that asks to find integer values of n for which $$x^{2}-1=n!$$ http://en.wikipedia.org/wiki/Brocard's_problem. According to Brocard's problem ##x^{2}-1=n!=5!*(5+1)(5+2)...(5+s)## here,##(5+1)(5+2)...(5+s)=\mathcal{O}(5^{r}),5!=k##. So, ##x^{2}-1=k...

I was watching a discussion on wether the the universe is the way it is through design or by chance. The design theory is basically that the universe is such a complex entity and that for it to have evolved exactly as we see it, then it must have been designed. The counter theory is that we live...

This is an excerpt from "Introduction to Mechanics" by Kleppner and Kolenkow: "The reason why gravitational force vanishes inside a spherical shell can be seen by a simple argument due to Newton. Consider the two small mass elements marked out by a conical surface with its apex at ##m##. The...

Hello 1. Homework Statement Consider fk N*→N, k≥0 fk(n)=Σ jk n>0 We're looking to establish these identities, using a combinatorial argument fk(n)=n if k=0 fk(n)= 1/(k+1) [ nk+1 + Σ ( i , k+1) (-1)k+1-ifi(n) ] if k>0 the sum is about i from i=0 to i=k-1 and (i, k+1) is the combination...

Hello all! My class is doing a an argument essay that requires students to choose a topic that is specific and has two sides. My problem is that I can't seem to find a topic that fits this criteria. I was hoping to find a topic in technology. One topic I really wanted to research was artificial...

Homework Statement Find the principle argument Arg z when z = (sqrt(3) - i)^6 Homework EquationsThe Attempt at a Solution I'm sorry to say that I'm not sure how to solve this problem. It's my understanding that what this question is basically asking me to do is find theta such that...

1. In the part of the analytical solution of the harmonic oscillator, p38 in my version of the book a certain mathematical trick is used. The position part of the wave function in function of a dimensionless variable z, is given by ##\frac{d^{2}\Psi(z)}{dz^{2}}=(z^{2}-K) \Psi## In the limit of...

Hi everyone, How hybrid functional can be quicker than HF ? Because we have to use the HF exchange part, so we have to solve the problem with HF before, am I right ? Thank you

After reading some of Einstein's writings on relativity I am confused as to why he finds it necessary that the universe is finite. In his "Relativity", Einstein explains that the ultimate Newtonian picture of the universe (matter in Euclidean space) would be one in which all mass were...

A question about time dilation.. I find myself in an argument / discussion about the theory of time dilation, and it seems to me, that the terminology is really the problem. Would it not be more accurate to say that the effects of time slow, as speed increases ? To say that our test of clocks...

I wanted to exchange some opinions about worm gear enveloping. I am designing a worm gear 3d model and, putting the appropriate amount of thought in it, some interesting points arise. One may either: 1) Envelop (is that right?) the worm gear helix, so that its radius increases from the gear's...

Do the logicians/mathematicians agree with the picture's claim?

Hello, I have the point ##-1 + 2i##, for which I am asked to find the modulus and argument. The modulus was simple enough, but I am having difficulty finding the angle. The point is located in the 4th quadrant, and so I need to make certain that I calculate an angle in the range ##(\frac{3...

After some integration, i am getting a form e^{i \alpha\phi+i\beta\phi\sin(\phi-\phi')-i\gamma\sin\phi} , where ##\alpha, \beta, \gamma## are constants. Now i want to apply the limit where ##\phi ## ranges from 0 to ##\infty ## (ya, in the argument of sine we will encounter ##\infty ## which is...

Quick question about translating what's on the Velocity vs Time graph into what is actually happening to the object. A cart is traveling on a straight horizontal track. So I determined that east is positive direction. So, if the velocity vs time graph is showing a negative slope of -0.2 does...

Homework Statement Calculate argument of complex number -1-\sqrt{3}i Homework Equations The Attempt at a Solution The argument of this is -120 degrees but why couldn't we as well say it's 240 degrees? Since going 240 degrees will go to the same point as -120 degrees. Why is this false?

I am doing some work on the fine-tuning argument (FTA), basically P(D|F\&B)>P(D|B) where D is the hypothesis that the physical constants were in some way designed (to make life possible, for example), B is shared background information and F is the observation that the physical constants...

Hi I am kind of lost Deside an argument for w w= (-4(√3+i))/(-1+i) I know that the arg is the angel.. And the equation is in radians.. where to start?? best Regards! Homework Equations The Attempt at a Solution

Every general explanation of the quantum zeno effect I've found is (from my perspective) so full of gaps that I cannot understand the explanation. My understanding has improved due to responses to a previous post on this topic as well as to a detailed but still gappy paper that was recommended...

I had an undergraduate pose an interesting question to me. "Why doesn't Cantor's Diagonal Argument apply to the rationals?" http://www.proofwiki.org/wiki/Real_Numbers_are_Uncountable/Cantor%27s_Diagonal_Argument Now obviously it doesn't since the rationals are countable. But what breaks...

In the wiki, I found this definition for the argument: http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Exponential_definitions However, in other page of the wiki (http://en.wikipedia.org/wiki/Complex_conjugate#Use_as_a_variable), I found this definition for...

matlab halp! fplot() with 3-input argument function?? Homework Statement heres da link: http://postimg.org/image/uqqr3q0k3/ don't really need to look at that though. Its just a function in another file, I have to call it but it takes 3 input variables, problem with fplot is it only uses a...

Every general explanation of the quantum zeno effect I've found is (from my perspective) so full of gaps that I cannot understand the explanation. I am wondering if anyone can help me fill in the gaps here? The most detailed explanation I've found runs something like this: Let |ψ0> be the...

The explanation below illustrates why I think the method of successive approximations is merely a sneaky way of working with power series when you're not formally allowed to use a Taylor series expansion for a function (i.e. when it doesn't exist, as in proving the existence theorem on ode's for...

I love my little girl and so does her mom but she needs to understand.

Hello, I would like to check if the work I have done for this problem is valid and accurate. Any input would be appreciated. Thank you. **Problem statement:** Let $G$ be a group of order 150. Let $H$ be a subgroup of $G$ of order 25. Consider the action of $G$ on $G/H$ by left...

First sorry if this is to some extend kind of against the rules, especially considering that technically this thread is debating pseudoscience. I just need someone with "scientific credentials" to backup my argument. The issue is about a certain Royal Raymond Rife's apparatus supposedly able to...

Now I think there are arguments for the Fine Tuning of the universe. I like Martin Rees' book but I know there are others who disagree with what he said in his book (Just Six Numbers) On another forum I've got involved in a discussion on this topic and I've seen an argument that I think has no...

When I learned about derivatives I was taught to put the absolute value sign around the argument for ln and log. For example \log{|x|} and \ln{|x|} instead of log(x)ln(x). Does this make a difference? Should both brackets and the straight lines be used? When taking the derivative what is the...

Hello! So I have questions on this equivalence: Imlog[(1+x)/(1-x)] = arg [(1+x)/(1-x)] where x: complex number How is this true? Is it always applicable no matter what form of complex function is under calculation? Thank you.

Dear All Firstly, thank you for looking at my post. I am so close to a solution to a problem that has been given me a massive headache. I am also very stupid and was wondring if one of smart guys could take a look at my problem and see if you might be able to help. I am trying to...

I am sure you are all familiar with this. The number generated by picking different integers along the diagonal is different from all other numbers previously on the list. But you could just put this number as next element on the list. Of course that just creates a new number which is missed...

I've been studying for a test and have stumbled upon another type of problem I'm not comfortable with yet. I need help applying the argument principle - the practice problems in my textbook all consider only polynomials in the first quadrant. In solving this type of problem I consider...

Hello. I'm not terribly proficient with Bessel functions, but I know that those of the first kind are given by \begin{eqnarray} J_n(x) & = & \left(\frac{x}{2}\right)^n\,\sum_{\ell=0}^\infty\frac{(-1)^\ell}{\ell!\,\Gamma(n+\ell+1)}\,\left(\frac{x}{2}\right)^{2\ell}, \end{eqnarray} where...

My grade 11 textbook never mentioned about inertial frame, non- inertial frame, rotating frame of reference and so son.The derivation of centripetal acceleration was very intuitive.This derivation was given after Laws of Inertia and other Newton's laws of motion.Ideas like cross product and dot...

Homework Statement . I want to prove that there is one solution for e^z-z in every shifted copy of the fundamental strip by applying the argument principle to the boundary of a rectangle −M≤Rez≤M , 2kπi≤Imz≤2(k+1)πi for large M and integer k . I need help in using the...

Homework Statement Sketch the locus of points in the argand diagram defined by z: arg (z-1) - arg(z+1) = ∏/4 Homework Equations The Attempt at a Solution By simple geometry i worked out that at a point in the x-y plane, the angle subtended from that point to -1 and 1 must...

ℂI am working on an assignment and have come across a question that I'm not quite sure how to approach. Here it is, with my "solution" and reasoning: "[F]ind the limit at ∞ of the given function, or explain why it does not exist. 24. h(z) = Arg z , z \neq 0" (Complex Variables Second...

Determine the interior, boujdary, and closure for the set: { 1/n : n is in the positive integers Z}. Attempt: two things bothering me. 1) if i am in the set of positive integers, how does 1/n even exist? 2) now let's say it does exist, then the inteior would be empty because every...

If any application of probability and statistics dosen't imply that particular proces dosen't have deterministic laws, then how quantum physicists come up with an idea that determinism is false ? P.S. I am second year bachelor student of applied physics and I will have quantum physics course...