Cut Definition and 266 Threads

Hi there! I'm trying to prove that every Dedekind cut A has an additive inverse -A such that A + (-A)=0*. We've defined addition of cuts A and B to mean A + B= {a + b|a belongs to A and b belongs to B} and 0*={x|x<0 and x belongs to Q}. Now, it seems fairly clear that the additive inverse of...

Why do we need to normalize vectors for? Is it just to cut down on the arithmetic when finding other quantities of the vector? Does it make life simpler to normalize vectors?

I need help with the last part of Problem 20, Chapter 1 of Rudin. Here's the problem: "With reference to the Appendix, suppose that property (III) were omitted from the definition of a cut. Keep the same definitions of order and addition. Show that the resulting ordered set has the...

What's with this guy? He seems to begin everything by saying (basically) "I'm a doctor, so therefore, in conclusion <blank>" He did it when he wanted to cut Planned Parenthood, & I bet he tried it during the healthcare reform debate a year or two ago also. I wonder if this doctor understands...

IMO, the only way to effectively cut our deficit is to cut spending ASAP and to keep all future spending on-budget and transparent. We can get rid of a lot of spending with a few moves. First, close at least 600 foreign military bases. They are not necessary to the security of our country...

Hi there Just a quick question; when I'm calculating moments in a cantilever beam (in my case a quarter circular one), is there any reason (apart from my own ineptitude) why I shouldn't be able to make the cut and FBD starting from the fixed end? I get different answers when I make the cut...

Hello, I am trying to understand an equation stated in the book 'Principles of Protein X-Ray Crystallography' by Jan Drenth (The exact page I am reffering to can be found here...

Hi PF! I've been trying to find out how one could find which z-coordinates to 'cut' at to get a specific volume of the sphere cut off. i.e. I have a unit sphere, therefore the total volume is (4/3)*pi*r^3, where r = 1. Now I want to get 1/4 of that volume cut off. So, (1/4)*(4/3)*pi*r^3...

Homework Statement Compute this determinant \begin{vmatrix} 1 & 1& x& 1\\ x& 1& 1 &1 \\ 1& 1 & 1 &x \\ 1& x & 1& 1 \end{vmatrix} The Attempt at a Solution I tried swapping rows and eventually I got -\begin{vmatrix} x & 1& 1& 1\\ 1& x& 1 &1 \\ 1& 1 & x &1 \\...

I'm really good at math, but I'm horrible at hands-on stuff. I can't build things; for example, I couldn't even assemble my bed without help. I had no idea how to do it even with a manual. My dream is to go into EE but I don't know If I can do it. I know I can do CS, but I'd rather do EE. Am...

Hi, I am currently a freshman majoring in Mechanical Engineering in the nuclear track. I really like math, but I've been having a hard time with Calculus I this semester. My teacher isn't great, but I'm just worried I'm not cut out for engineering if I'm already having trouble with Calc I. I'm...

I know the cut off ratio is of the specific volumes, but is that it? And what exactly do they tell you

Homework Statement A thin plano-convex lens of focal length f is split into two equal halves. One of the halves is shifted along the optical axis as shown. The separation etween the object and the image planes is 1.8m and the magnification of the image formed by one of the half lens is 2...

Eric Cantor's YouCut now poised to cut down "questionable" NSF grants http://scienceblogs.com/tfk/2010/12/asshat_eric_cantor_readies_tro.php Hmmm... I'm pretty sure that the following comment might temper some initial anger: (if the non-scientifically educated were actually good at...

We have a poll about extending the Bush tax cuts, so I thought it might be interesting to have this one to go along with it. :smile: Your paycheck is about to shrink My wife and I must be among the few people who actually saw this "stealth tax cut" because we got an unanticipated refund for it.

Consider the usual phi^4 theory, when we derive the Lehmann-Kallen representation of the propagator, by inserting a complete set we know that the propagator has a branch cut starting from 4m^2, where the m is the physical mass. My question is: what's the construction of these...

I wanted to get opinions on whether solving this problem in a non-numerical way is realistic, or if someone has the answer, all the better. I have a totally arbitrary ellipsoid (not aligned with any axes) that I can describe by matrix A, like x'Ax=1 is the ellipsoid surface. I have the points...

Homework Statement Find the area of the portion of the cylinder x^2 + y^2 = 2x that lies inside the hemisphere x^2 + y^2 + z^2 = 4, z \geq 0. Hint: Project onto the xz-plane. Homework Equations I want to use the formula for surface area \int\int\frac{|\nabla f|}{|\nabla...

Ola, If we have two curves, and they cut them selves in a way like these two: y=x^2 and x^2+(y-1)^2=1. Does it always mean that those two curves in a cut point would have a same tangent, in other words do they need to have the same derivative in that spot? Thanks!

The name "Tea Party" is a reference to the Boston Tea Party of 1773—a protest by American colonists against various acts by the British Government which, among other things, attempted to establish a monopoly on the importation of tea into the colonies by giving a cut on re-importation tax...

For some crimes, it seems the death penalty is not punishment enough. I am for the death penalty in cases, such as this, where there is no question of guilt. But I also agree that in these cases, the death penalty should be carried out immediately after sentencing Would you agree or...

Homework Statement Find the x- and y-coordinates of the center of gravity of a 4.00 ft by 8.00 ft uniform sheet of plywood with the upper right quadrant removed as shown in the figure below. The dimensions of the cutout are a = 3.50 ft and b = 2.10 ft. The Attempt at a Solution I made...

Hi, I am independently learning analysis, I found videos online and Rudin's textbook, though I am unclear on one thing. I thought the point of dedekind cuts was to construct the reals without explicitly talking about the irrationals, which is why to get at the square root of 2 you let the cut be...

Hello! I've seen volume calculations involving cutting a wedge from a cylinder where the wedge cuts down to the centre of the circle (i.e. the length of the straight edge will be the diameter of the cylinder). I was looking for hints on working out the area of a wedge cut from a cylinder where...

I use a DSL modem from At&t and it has provided me with so much joy I can barely contain myself. :rolleyes: Over the last six months or so and I have noticed that despite my paying for 3mb down I usually got .9 to 1.5 on average, but after several days it would slowly dwindle until it finally...

In response to LA's threatened boycott of all things Arizona, an official of Arizona's version of a Public Utilities Commission (http://www.azcc.gov/divisions/administration/about.asp" ! This is getting uug-lee..

Homework Statement I'm finding the residues of the branch cut of \int^\infty_0 \frac{dx}{x^{1/4}(x^2+1)}dx Homework Equations The Attempt at a Solution I am trying to find the residue of i I am not sure how to handle lim z->i of \frac{1}{z^\frac{1}{4}(z+i)} Any nudges...

http://www.elastoplast.com.au/media/11/12276804863360/schnittwunde_03.jpg If your skin is cut deeply, meaning a cut to dermis why is that we can see scar tissue. I mean if the cut region in the dermis would be replace by scar tissue, but the epidermis region above that would have normal...

Homework Statement Branch cut for cos(sqrt(z)). Homework Equations The Attempt at a Solution Apparently there is no need for a branch cut for this function, but I am not sure why - I heard it has something to do with cos being an even function. Any clarification would...

I have been interested in how Gyroscopes work and now have a question about this video: http://www.youtube.com/watch?v=8H98BgRzpOM&feature=related If we spun such a wheel up to speeds close to the speed of light, what would happen if we cut the rope off? After some pondering, using my little...

Guys, I have two questions: (1) what does a vanishing Fermi energy mean? (2) I have also calculated the phonon self energy for the electron phonon interaction in graphene. However in one of the papers, they state that one needs to subtract from this self energy the case of vanishing Fermi...

does electrons fall out when a current carrying wire is cut well i know it doesn't make much sense n also doesn't have ny effect but still does it happen or not ?

A simple way to cut medical cost would be to limit medical care to only items that were widely available in 1960. Do not fund any drug, surgery, procedure, etc. Life in 1960 was OK. People did not die in the streets. Unless we are saying people are less healthy today than 1960 this should...

This semester my university has a lot of PhD students that are to afraid to graduate or can't be supported by their professors due to a lack of funding. So because of this there are a lot of PhD students forced to teach this semester. Of course this means that there is a huge flood of TAs this...

In the expression ln(-s^2-i\epsilon) , s^2 and \epsilon are positive (this expression can result from for example a loop diagram where s^2 is a Mandelstam variable). In mathematics, the branch cut of ln() is usually taken to be the negative real axis, so that the value above the negative axis...

Hi with respect to the bremsstralung and the Xray emission, i have a graph of the xray emmision and at the end of the bremsstrahlung, at roughly 35 KeV,there is a sharp cut off. Is the reason for this because that 35KeV is the maximum energy of the incident electrons, and hence no photon...

So I had a random thought come to mind today (I've been studying magnetics in general physics lately)... If you cut the Earth in half, evenly, from pole to pole and allowed the two hemispheres to rotate freely about the plane of the cut, but not to deviate away from each other, what would...

Homework Statement A rod of length 69.0 cm and mass 1.70 kg is suspended by two strings which are 43.0 cm long, one at each end of the rod. http://schubert.tmcc.edu/res/msu/physicslib/msuphysicslib/20_Rot2_E_Trq_Accel/graphics/prob13a_1016full.gif (A) The string on side B is cut. Find...

I'm having problems with this question. A piece of copper wire has a diameter of 0.389mm. If copper has a density of 8.92g/cc, how long (in meters) should you cut a piece of wire to obtain 0.0141 moles of copper? I tried finding the volume of the cylinder and other things, but I'm...

My friend needs to clean his head light lenses and they are plastic , does anyone know a chemical that will dissolve plastic or clean the lens to cut the oxidation , i could buff the lens but i would rather use a chemical, I was thinking along the lines of lacquer thinner.

If I have this graph: http://rpi.edu/~doriad/graph.png Node 0 is the source and Node 3 is the sink. Is the min cut 11 (the minimum sum of capacities of edges cut to partition the graph into two parts)? There are two min cuts, correct? One that separates 0 from everything else, and the other...

im really drawing a blank on this one... been a while since i done timers and its late! im totally lost i need help designing a varible timed circuit cut off, but it needs to be activated by a push to activate switch. the timing on this literally needs to be 1-2 possibly even 3...

I am doing the second half of my first year of university (I'm in the southern hemisphere). I"ve tried to keep my options open, taking the required papers for several fields of engineering, as well as physics, chemistry and maths... I am leaning very strongly towards Engineering for the...

I was able to get my electricity bill down to about half of what it was at this same time last year. It was not anyone change I made, but all of these things together that made the difference. As a note, I live in Texas where heat is the issue. Warming the house in the winter is no big expense...

Hello! Im writing a technical report with "article" as documentclass in Latex How can I cut off a line? I have a long piece of text and I want to cut it of like a new paragraph how do I do that? I have tried to use // but that's wrong... thanks

Hello! I got a very long equation that I´m writing in Latex, it is so long that the equation reference can´t fit on the same line. How do I write to cut the equation so it continues on the next line? Thanks

Homework Statement Find the area of the two regions in which y = mx divides x2+y2-2ax < 0. Homework EquationsThe Attempt at a Solution I was thinking of the following: \int_{0}^{2a}\int_{\sqrt{2ax-x^2}}^{mx}dy\:dxThanks for your help!

to the physics majors out there...do/did you find that although your work is challenging, it is extremely rewarding and worth struggling over? i recently decided on a physics major and will be hitting the heavy courses next year

Maybe cut isn't the best word, but you get what I mean. Surely if all the negative polar molecules move to one side of the magnet and the positive polar molecules move to the other side, and you cut the magnet in the middle, you shouldn't get two more magnets? I'm still only doing high...

Homework Statement a rectangular box with no top is formed by cutting out equal squares from the corners of a square sheet of metal, 10 cm by 10cm, and bending up the 4 sides. What size of square must be removed from each corner to generate a box with a volume of 50cm^3? (Note: there are 2...