Dimension Definition and 908 Threads

My question, because I keep seeing this on the internet, is that if S is a subset of R and Hausdorff dimension greater than 0, it is uncountable... is this true. It seems not to be. If one were to modify the Cantor third set and remove some length of 1/n from the middle of the sets at each...

In its final trip upstream to its spawning territory, a salmon jumps to the top of a waterfall 1.9m high. What is the minimum vertical velocity neeeded by the salmon to reach the top of the waterfall? This uestion has no velocity so, do you think that final velocity is Zero... solution...

Hi to all, I have a problem to share with you guys. How can I calculate the thickness of my solenoid if I have these values; Solenoid long : 20cm magnetic field, B : 5Tesla Current, I : 20A Thanks a lot for your help. I appreciate that

i need some help here, say if there's a ship, no matter how it steers, it will always end up at the starting point, becauses it is in a new dimension, but how do i go about explaining it? thanks!

I'm confused about how to understand the ct dimension. I cannot get passed thinking that physically real dimensions mean more degrees of motion. If a flatlander went to the store to buy a can of Coke, the closed container would be a circle. The container is closed simply because there...

new to physics and my first question first,i am a nearly newbie high school student in physics, please i would like to learn physics from the internet enough to let me think ?...also i have a question in dimensions and please anyone explain how can you measure the 4d of matter although (i...

Alright, I'm in my first QM course right now, and one of the topics we've looked at is solving the one-dimensional time-independent Schrodinger equation for various potentials, such as the harmonic oscillators, infinite and finite square wells, free particles, and last, but not least, the dirac...

subspaces and dimension! Consider two subspaces V and W of R^n ,where V is contained in W. Why is dim(V)<= dim(W)...? "<=" less than or equal to

Find the Dimension of the null space of the given matrix A: | 1 3| |-2 -6| The Attempt at a Solution I honestly don't know how to work this at all. I think I'm confused as to what Null Space actually is, so that's making this a difficult problem to understand. please help.

Homework Statement Given the vectors: x1=(3,-2,4), x2=(-3,2,-4) and x3=(-6,4,-8) , what is the dimension of Span(x1,x2,x3) Homework Equations The Attempt at a Solution I know x1,x2 and x3 are Linearly dependent since its determinant is zero. There are a total of 3 vectors in...

Homework Statement bloks b and c have m asses 2m and m respecti vely, and are at rest on a firctionless surface black a also of mass m.. is heading at speed v toward block b as show... determine te final velocity of each block after alll subsequent collisions are over, assum all collision are...

Is it a fact that in an infinite dimensional normed linear space, the closed unit ball is never compact? If so, how does one go about seeing this?

Homework Statement Given x_{1}= \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix}, x_{2}= \begin{pmatrix} 3 \\ -1 \\ 4 \end{pmatrix}, x_{3}= \begin{pmatrix} 2 \\ 6 \\ 4 \end{pmatrix} Find the dimension of Span(x_{1}, x_{2}, x_{3}) Homework Equations If V is a vector space...

Okay how can someone explain the four dimension in so that someone like me can under stand them? I'm asking this question because my math teacher will not talk about it so that the other students would not get confused. I get the theory (or how ever you want to say it)a little bit but i still...

Hello, I am in the process of reading Black Holes, Wormholes & Time Machines and am somewhat confused, even though it is aimed at people like myself who have very little knowledge on the subject. I am reading about the 4th dimension now but I do not understand the relevance of researching into...

Homework Statement Suppose that U and V are finite-dimensional vector spaces and that S is in L(V, W), T is in L(U, V). Prove that dim[Ker(ST)] <= dim[Ker(S)] + dim[Ker(T)] Homework Equations (*) dim[Ker(S)] = dim(U) - dim[Im(T)] (**) dim[Ker(T)] = dim(V) - dim[Im(S)] The Attempt at a...

In Hartshorne's book definiton of a dimension is given as follows: İf X is a t.s. , dim(X) is the supremum of the integers n s.t. there exist a chain Z_0 \subsetneq Z_1...\subsetneq Z_n of distinct irreducible closed subsets of X My question is: Can we conclude directly that any...

what is dimension of target space?? is it the R^4 on top(which says that we have 4 coordinates like x y z t or 4 vectors in the matrix (whats it called the total number of the vectors??)

See the New Scientist article on how the explosive evaporation of primordial mini-black holes could prove the existence of extra dimensions. http://space.newscientist.com/article/dn13279-exploding-black-holes-could-expose-hidden-dimensions.html

I have no schooling in physics but for the past 3 years I have had this idea floating around in my head and figured i'd tell somebody and see what they thought. my theory is about the 4th Dimension. I believe that energy is the 4D and not time. Energy can be measured like width, heigth and...

[SOLVED] Motion in one dimension Homework Statement To protect his food from hungry bears, a boy scout raises his food pack with a rope that is thrown over a tree limb at height h above his hands. He walks away from the vertical rope with constant velocity V^{1}_{boy}, holding the free end of...

Let's say the universe exists as a collection of related static 3-d spaces, like in Julian Barbour's book The End of Time. Nothing ever actually moves. The illusion of movement comes from moving from one of these spaces to another which is closely related to the previous one. It's similar to the...

A car traveling at 16.0 m/s runs out of gas while traveling up a 21.0 degree slope. How far up the hill will it coast before starting to roll back down? I tried 1/2mv^2=mgh 1/2(16)^2=9.8h 13.06=h can anyone confirm if this is correct or not. I;m not sure if I have to use trig to...

Homework Statement Hai Friends, i want to know the complete the dimension of bevel gear front teeth width and end teeth width. How this dimension are related with emperical formulas please give me complete detailing of bevel gear far straight and spiral also...

[SOLVED] Dimension of column- and rowspace Homework Statement My book doesn't answer this question clearly, but I have notived the following connection: Does the dimension of the rowspace of a matrix equal the dimension of the columnspace of a matrix which equals the rank of the matrix?

Select ALL the valid statements, i.e., B, AC, BCD. If an equation is dimensionally A) correct, the equation must be correct. B) correct, the equation may be wrong. C) incorrect, the equation may be correct. D) incorrect, the equation must be wrong. E) correct, the equation may be correct...

Consider that you have derived the Lorentz transformations in one space diomensions x=g(x'+Vt') t=g(t'+Vx'/c^2). In order to extend the problem to two space dimensions many Authors add y=y'. Please tell me if that is the best approach. Thanks.

Edward Witten on LQG "for lambda > 0, QG does not exist in any dimension" arxiv.org/abs/0706.3359 - page 6 "for lambda > 0, QG does not exist in any dimension" ...the reason... "cannot provide precise observables" As I understand Edward Witten, deSitter space is not stable but metastable, and...

Find the dimension of the solution space of Ax=0, where A=1 2 5 -1 3 1 is the rank(A)=2 so the nullity(A)=2? is this correct?

What is the exact definition of the dimension of a topological space?

Everyone "knows" that the fine structure constant (alpha) is a dimensionless number, but I am troubled by the fact that the Planck unit of resistance must be one - if that is true - and that strikes me as suspicious. I wonder if anyone can shed any light on this. I present the complete...

Homework Statement Two masses hanging vertically from a pulley are each initially 1.6 m above the ground and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? Homework Equations \vec{F}_{net} =...

Ok I am stuck on how to solve this problem and i don't have physics again until next week. The question is: A ball is thrown horizontally at 22m/s from the roof of a building lands 36.0m from he base of the building. How tall is the building?

Find the dimensions of the soultion space of Ax=0, where A= 1 2 5 –1 3 1 (A is a 2x3 matrix). To find the dimension you have to subtract n from rank(A) //n being the number of columns 3-2=1 The dimension of the solution space is 1. is this correct?

I wasn't sure where precisely to put this, hopefully it gets an answer here. In my computational physics class we just learned about the correlation dimension. I know how to compute it, but don't quite know what it means. I learned roughly that the correlation dimension of something is a...

Given the vector space consisting of all bilinear forms of a vector space V (let's call it B) it's very easy to prove that B is the direct sum of two subspaces, the subspace of symmetric and the subspace of skew symmetric bilinear forms. How would one go about determining the dimension of these...

It don’t get much weirder than this. The universe is about to lose its dimension of time says a group of theoretical astrobods at the University of Salamanca in Spain. And they got the evidence to prove it. [..] This ain’t entirely bonkers and here’s why. Bars Mars has calculated what it’s...

hi, I have to find the dimension of the constant C2. I have no problem with finding constant C1. Here is the question, and I appreciate your help. the equation is : m= \sqrt{\frac{2t}{C1}}+m cos(\frac{1}{C2}t) I would like please to understand the solution with knowing the exact...

Why does does the following code not compile? PROGRAM TYPES INTEGER A(3) A(1)=1 A(2)=2 A(3)=3 CALL SUBR(A) print *,'Done' RETURN END C --- Here is a subroutine ----- SUBROUTINE SUBR(A)...

Homework Statement A quarterback claims that he can throw the football a horizontal distance of 184 m. Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 29.7 ° above the horizontal. To evaluate this claim, determine the speed with which this...

Hey guys, Does dimension remain unchanged under a linear map? Ie if i have a map f:U->V does dim(U) = dim(img(f))? Cheers -Z

-------------------------------------------------------------------------------- A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of 8m/s at an angle of 20 below the horizontal. It strikes the ground 3.00s later. The horizontal distance at which...

A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of 8m/s at an angle of 20 below the horizontal. It strikes the ground 3.00s later. The horizontal distance at which the balls strike the ground from teh base of teh building and the height from...

Homework Statement Describe in words the region of R3 (3 dimension) represented by the following inequality. 1)xyz=0 Homework Equations none i know of The Attempt at a Solution no idea where to start. I know that this means one variable must be equal to 0, but i don't...

Homework Statement #1 Runner A is initially 4.0 mi west of a flagpole and is running with a constant velocity of 6.0 mi/h due to east. Runner B is initially 3.0 mi east of the flagpole and is running with a constant velocity of 5.0 mi/h due west. How far are the runners from the flagpole...

...may frighten small children http://youtube.com/watch?v=6T0UQfKTcQw

In magnetism , mH = F, where m = pole strength ; H= magnetic field intensity ; and F = Force. F = [ MLT^{}-2] Proof that dimension of mH = [MLT^{}-2]

Homework Statement I am learning linear algebra (basic) and using Lang's book. In talking about vector spaces (finite dimensional only), it is easy to understand what is the dimension of the vector space (i.e. the number of elements in any basis). But I met the following case (not a vector...

What is the meaning of dimension? It is my understanding that dimension related to the measuring out of something. If there is some observable phenomena that we can measure by defining units of measure and counting the quantity of these units that there is an associated dimension which is not...

A new DIMENSION?? To Support the Theory of going into another dimension by traveling through a Black Hole. Since Scientists say you can go to another dimension through a Black Hole, why not you go to another dimension by just going pass a Black Hole?:confused: