Property Definition and 608 Threads

Hi, my question is sort of a general work problem. using that work is equal to the integral from x initial to x final of F dot dl, I'm having trouble trying to visualize why this works for a spring. assuming, for example, a spring is stretched from equilibrium, the force of the spring is...

Homework Statement If E has finite measure and \epsilon>0, then E is the disjoint union of a finite number of measurable sets, each of which has measure at most \epsilon. Homework Equations The Attempt at a Solution I proceeded by showing that by definition of measure, there is a...

Let A,B be mxn matrices and C be nxk matrix. What is the necessary or sufficient condition such that AC=BC implies A=B ? In my work, A and B are m by m matrices and C is just a column vector m by 1. In this specialized case, what are the condition imposed on the elements of C such that AC=BC...

Homework Statement how come that 16/64=.25 166/664=.25 1666/6664=.25 and any 1then n number of sixes / the same number of sixes then 4 = .25 same thing with 19 / 95 is there other strange division patterns?

Homework Statement Provide an example that shows why the reflexive property is not redundant in determining whether a relation is an equivalence relation or not. For example, why can't you just say, "If xRy then yRx by symmetric property, and then using transitive property you get xRx."...

Homework Statement Suppose the function f has the property that |f(x) - f(t)| <= |x - t| for each pair of points x,t in the interval (a, b). Prove that f is continuous on (a, b). Homework Equations I know a function is continuous if lim x-->c f(x) = f(c) The Attempt at a...

Must the ground state in an even potential of one dimension be the even parity?

I have a query regarding Specific Volume, which is a property of a substance. I don't get why it is considered as an Intensive Property. It IS dependent on mass (SV = m/density) and hence I think it should be an Extensive Property. Could someone explain pl?

I am trying to understand the following theorem: An ordered field has the least upper bound property iff it has the greatest lower bound property. Before I try going through the proof, I have to understand the porblem. The problem is, I don't see why this would be true in the first...

If pq=ab where p, b are relatively prime, p must be a factor of a and b must be a factor of q.

Homework Statement Prove the Archimedean property Homework Equations Know what a least upper bound is The Attempt at a Solution Assume that if a and b are positive real numbers, na≤b for all natural numbers n. Then the set S of all numbers na, where n is a natural number, has b...

Hey guys, sorry for practically flooding the forum today but I have an analysis exam and nobody is more helpful than phys forum folk. I am having trouble understanding a line in Rudin. Thm 2.36: If {K_{\alpha}} is a collection of compact subsets of a metric space X s.t. the intersection of...

Homework Statement Homework Equations Continuity @ v0 The Attempt at a Solution Using the epsilon delta definition of continuity: If we choose epsilon such that epsilon < a, then |f(v) - f(v0)| < a. So f(v) is in the interval (f(v0) - a, f(v0) + a). Only half of this interval is what I want...

For all k \in N, f(2k + 1)= f^{2}(k) + f^{2}(k + 1) I couldn't find this one in the forum... I am stuck on the induction step, really I have no idea how to get it going. Oh, and the k statements should be in subscript, I was having real problems with LaTex, misreading subs and sups. Thanks...

Homework Statement Using the density of Q(rationals) in R(real numbers), prove the Archimedean property. Homework Equations Density of Q in R: For all x,y in R, and x<y, there exists q in Q s/t x<q<y. Archimedean property says: For every real number x there exists a natural number y...

I've searched these forums hardcore about these questions and the wide range of answers is so confusing to me, so I hope that maybe if I provide some examples and specific questions, I may better understand. I always hear that quantum particles exhibit "intrinsic" randomness in the states they...

I think I've cleared up a fundamental misunderstanding I've had for a while, and want to get confirmation I'm right. Is the following statement true? In QFT, a quantum field is not part of the state of a quantum system, and is not an aspect of reality that needs to be measured to be known...

Homework Statement I am just curious ? I have a feeling that completeness or the archimedean property relies on well ordering but I am not entirely sure. However, completeness funishes a supremum or infimum for any subset of R that is bounded above or below, respectively.The Attempt at a...

when solving physics problems we have to do various calculation to find a quantity but the results are different if we round up in every operation than if we round up in only the final operation? I never cared before but sometimes I see big differences especially when dealing with numbers with...

This from another thread (according to PF's rules, the quoted part belongs in that thread, but the follow-on part belongs in its own, separate thread): So: mheslep, yours is a very good reminder that market economies will render whatever new technologies at least as expensive as any...

What is the property of a particle known as spin? I ask this because I read somewhere that particles don't actually spin around and that no one really knows what spin is. If no one knows what spin is, how can we measure it?

How can prove this \exp(At)\exp(-At_0)=\exp(A(t-t_0))? using \displaystyle\sum_{i=0}^n{(1/k!)A^kt^k} and this properties in t=0 [\exp(At)]_{t} = I exp(At)exp(-At)=I \frac{dexp(At)}{dt}=Aexp(At)=exp(At)A

Homework Statement Identify integral as the mean value of a harmonic function at a point and evaluate the integral: \frac{1}{2\pi} \int_0^{2\pi} \; cos(1+cos(t)) cosh(2+sin(t)) \; dt Using: u(x_0,y_0) = \frac{1}{2\pi} \int_0^{2\pi} \; u[x_0+rcos(t) , \; y_0+rsin(t)] \; dt...

If i were to simplify ln(c*e^{-kt}) what happens? do I get c*(-kt) or ln(c) * (-kt) or something else? I'm not sure

Homework Statement prove the following if a is an odd integer, then, 24 l a(a2-1) (i'm not familiar with modulo yet, i think it can help, but let don't use it yet ;P) Homework Equations n/a The Attempt at a Solution i stumbled when using 2n+1=a for all integer n, because i will only get...

Homework Statement proof the theorem if a l b and b l a then a=+-b Homework Equations The Attempt at a Solution there exist integer p,q such that ap=b and bq=a, then I've no idea how i can relate it to a=+-b.. clue please T_T

I just learned the Brouwer fixed-point theorem of dimention 1 and 2.But the exercises make me sad,I can't solve them. Suppose X and Y are of the same homotopy type and X has the fixed-point property.Does Y also have it?

Homework Statement Scanned and attached Homework Equations I am guessing a combination of induction and the telescoping property. The Attempt at a Solution I'm studying this extramurally, and I've just hit a wall with this last chunk of the sequences section, so if someone can...

Homework Statement Let f be a C1 function on [-pi,pi]. Prove the Fourier coefficients of f satisfy |an| <= K/n and |bn| <= L/n n=1,2,... Homework Equations an = 1/pi * int[-pi..pi] (f(x)*cos(nx)) dx bn = 1/pi * int[-pi..pi] (f(x)*sin(nx)) dx Sorry if my form is slightly...

Hi there...I need ur help on these questions: 1) Can H2O exist as a vapor at -40oc,As a liquid? Why? 2) What would be the general nature of Constant volume lines on Phase (P-T) diagram? Both questions are from Engg. Thermodynamics-Moran,Shaprio(Things engg. think abt section) Also, does anyone...

Hello all, For a monotonic increasing/decreasing function f(x) on x \in \mathbb{R}, we can only have supremum/infimum which is occurred at x = \infty with value \lim_{x\uparrow \infty}f(x) Otherwise, if it was a maximum/minimum, it would violate the assumption of monotonicity. Am I...

I'm having a little trouble distinguishing the line between what the f.i.p implies and what it does not. **EDIT2** Hopefully this will make things more clear What I'm really interested in is a formal definition of the f.i.p regardless of the set in question or the field. Given the sequence...

if A is an n x m matrix where n < m I would like to prove that there exists some \lambda such that rank(A^T A + \lambda I) = m I know that if two of the columns of A^T A are linearly dependent, they are scalar multiples of each other and by adding some \lambda to two different positions, those...

If x_n\geq 0, y_n\geq 0 and \lim \limits_{n \to \infty }x_n exists, we have \limsup\limits_{n\to\infty}(x_n\cdot y_n)=(\lim\limits_{n\to\infty}x_n)\cdot(\limsup\limits_{n\to\infty}y_n). But if \lim\limits_{n\to\infty}x_n<0, do we have analog equation(I guess \limsup\limits_{n\to\infty}(x_n\cdot...

Hi: Is there a relation between k-connectedness ( meaning 1st, 2nd,..,k-th fundamental groups are trivial.) and having the homotopy-lifting property.? . This may be vaguely-related to being able to extend global sections from the j-th skeleton, to the (j+1)-st skeleton (j<=k...

I have a monoid (M,+), and I assume that for any two elements a,b in M it is always possible to find a third element k such that: a + k = b + k Is it possible to prove that M must be a cancellative monoid? In other words, can I prove that a+k=b+k \Rightarrow a=b ?

Diamagnetism is the property of an object which causes it to create a magnetic field in opposition of an externally applied magnetic field, thus causing a repulsive effect. This is property of all materials. But can be perceive only for materials which atoms or ions have closed shells. Examples...

1. Prove that for all boolean algebras if x+y=x+z and x'+y = x'+z then y=z. 2. Homework Equations : x+x' = 1, xx'=0, basically we are allowed to use the usual boolean algebra properties. 3.Attempt: This the second part of a problem, in the first part we had to give and example of...

once i was wondering that, how any property of an object describe an object??

Homework Statement Let x1, x2, and x3 be vectors in R^3. If x1 is orthogonal to x2 and x2 is orthogonal to x3, is it necessarily true that x1 is orthogonal to x3? Homework Equations I know that if x1 is orthogonal to x2 and x2 is orthogonal to x3, then... (x1)^T*x2=0 (x2)^T*x3=0...

this problem is from Apostol's Calculus Vol.1, i just started doing proofs so I'm still getting used to it. B - U (A) = ∩ (B-A) the U is the union of sets in a class F and ∩ is the intersection of sets in a class F. written under both the U and the ∩ are A∈F. so i let an element x ∈ B...

In the field of formal rational functions, construct a nest of closed, bounded intervals whose intersection is empty. (That is, show that the Nested Intervals property fails in this field) I know it has to involve radical 2 but because that is the only number we know is irrational but other...

I've encountered this question in some theoretical work I've been doing. Suppose you have two pdfs fH(x) and fL(x) with the same support (bounded or infinite... you can assume whatever you want about it). Suppose that the expected value of a random variable with pdf fL(x) is greater than the...

Homework Statement Prove that \delta(at)=\frac{1}{abs(a)}\delta(t) Hint: Show that \int\phi(t)\delta(at)dt=\frac{1}{abs(a)}\phi(0) (the limits of integration are from -inf to +inf btw, I couldn't find how to put them in..) Homework Equations The Attempt at a Solution Ok. I...

I have a question regarding the radius of convergence and hopely someone can help me with it. Suppose \SigmaNANZN-1 is given and if its primitive exists, will these two polynomials have the same radius of convergence?

I have so many fundamental questions about physics, i hope they are not considered "speculative" and deleted... Physics convolutes things so much, i wonder what does physics define as a physical property. For instance - an electron has a property (quality) of charge. Hopefully - this means...

What kind of sets exhibit the wada property? I know R2 does but does it extend to R3 or R itself?

Homework Statement Find three disjoint open sets in the real line that have the same nonempty boundary. Homework Equations Connectedness on open intervals of \mathbb{R}. The Attempt at a Solution If this is it all possible, the closest thing I could come up with to 3 disjoint...

Homework Statement Prove: If A is an invertible matrix and k is a positive integer, then (A^k)^-1 = (A^-1)(A^-1) ...A^-1=(A^-1)^k Homework Equations none The Attempt at a Solution I have a hard time proving this. How do I go about doing this? Any help would be great. I really...

tell me about colligative property?