Definition Definition and 1000 Threads

I've been thinking about the flat surface we call a plane. I've looked for definitions and none of the ones I have found satisfy me...in this respect...they seem dependent on assumed meanings and not self-dependent using only geometric contructions. Let me explain. One definition of a plane...

I was reading into traversable wormholes when I came across this definition from Matt Visser; 'If aMinkowski spacetimecontains a compact region Ω, and if the topology of Ω is of the form Ω ~ R × Σ, where Σ is a three-manifold of the nontrivial topology, whose boundary has topology of the form ∂Σ...

Watching a physics documentary I heard the following statement 'If an object falls into a black hole, what happens to its information'. I have a problem understanding the definition of information Is this. Information we could have gained through study? Or, Information governing particles at...

Can work be explained in following context- Work done is the amount of energy exchanged in executing an action through non-spontaneous method.

Homework Statement Confused about what a statistical ensemble actually means. Why does the ensemble have to have a uniform probability distribution at equilibrium? [If my definition of an ensemble is correct] The Attempt at a Solution This is what I understand so far: [/B] For any given...

Homework Statement ##f(x)=12x^2-5## The value of ##\lim_{h\rightarrow 0}\frac{f(x+2h)-f(x-3h)}{6h}## is ... A. 8x B. 10x C. 12x D.18x E. 24x Homework Equations ##f'(x) = \lim_{h->0}\frac{f(x+h)-f(x))}{h}## The Attempt at a Solution [/B] Looking at the problem question, it seems that it's...

Is the subset ##E## necessary in the following definition? It doesn't seem to serve any purpose at all and could've been written with ##S## directly? Isn't ##E## just another ordered set since it's a subset of ##S##? Definition: Suppose ##S## is an ordered set, and ##E \subset S##. If there...

Homework Statement gamma beam (γ) consequent of co 60 [this source have two beam; 1.1732mev(99.88%) & 1.3325mev(0.12%)] radiation behind the concrete block [ 300×300×20 cm] (thickness is 20 cm). analysis and plot Gamma-Ray Attenuation at 5 cm layers (4 layer) and plot spectrum of exited...

My professor says resistance depends on, R\quad =\quad \frac { \rho L }{ A } And is defined as, R\quad =\quad \frac { V }{ I } What does she mean? What is the difference? A definition is denoted by \equiv, what is the difference between that and an ordinary equal sign?

Hi guys, I'm having trouble understanding the definition of proper time interval, according to my book (Physics for scientists and engineers with modrn physics 10th edition serway jewett) the proper time interval "is the time interval between two events measured by an observer who sees the...

he definition of the limit of a function is as follows:[5] Let be a function defined on a subset https://upload.wikimedia.org/math/a/1/b/a1b67abab803e714098f3e69a33900da.png, let be a limit point of https://upload.wikimedia.org/math/f/6/2/f623e75af30e62bbd73d6df5b50bb7b5.png, and let be a...

Hi, I recently read that as temperature increases, atoms move faster and have higher frequencies, shorter wavelengths and more intense radiation. What does intense mean? Does it mean in a substance there are a greater percentage of atoms emitting at higher frequencies or does it mean another...

My textbook says: "if ## V = W_1 \oplus W_2 ##,, then a linear operator ## T ## on ##V ## is the projection on ##W_1## along ##W_2## if, whenever ## x = x_1 + x_2##, with ##x_1 \in W_1## and ##x_2 \in W_2##, we have ##T(x) = x_1##" It then goes on to say that "##T## is a projection if and only...

I'm studynig thermodymamics using the textbook 'Thermodynamics foundations and applications' (Beretta and Gyftopopulos). The definition of a system according to the authors consist in the specification of : -the costituents of the system ( atoms or molecules or prottons neutrons ... in...

why were quantities like momentum, force , potential energy, kinetic energy,work ,etc needed to be introduced in physics? and why were they defined the way they are defined?. would it not be possible to explain nature without defining these quantities or by using alternate physical quantities ?

In the book that I read, an operator is defined to be a linear map which maps from a vector space into itself. For example, if ##T## is an operator in a vector space ##V##, then ##T:V\rightarrow V##. Now, what if I have an operator ##O## such that ##T:V\rightarrow U## where ##U## is a subspace...

What makes an attractive potential "attractive"? I've just started learning about 1D S.E.'s with delta potentials and see the phrase frequently but am having trouble discerning a good, clear definition of what that means.

When I am creating an object via car audi audi=new car() what does the first line actually do? In non object oriented languages, some declaration like int mynumber to reserve a certain kind of bytes. But how does the compiler know what to reserve for the variable audi knowing it is of...

Hello, I'm reading a book on Lie group theory, and before giving the definition of a Lie group G, the author defines the concept of chart as a pair (U(g), f) where: i) U(g) is a neighborhood of g∈G ii) f : U(g)→f(U(g))⊂ℝn is an invertible map such that f(U(g)) is an open subset of ℝn. My...

What are gravitational waves in general, not just in the weak field/linearized theory?

This thread was triggered by @Anonymous Vegetable 's question re. nuclear fusion. In GR, energy density (in some coordinate system) is a parameter with physical implications- it is the (0,0) element in the stress energy tensor. This is in contrast with the situation in classical mechanics...

When the current is defined as being the conventional current then: i = dq/dt, i = integral of J*ds When the current is defined to be the electron flow: i = -dq/dt, i = - (integral of J*ds) Is this right?

On this wikipedia page https://en.wikipedia.org/wiki/Cone_(linear_algebra) , "a subset ##C## of a real vector space ##V## is a cone if and only if ##\lambda x## belongs to ##C## for any ##x## in ##C## and any positive scalar ##\lambda## of ##V##." The book in this link...

Hi guys, My question shouldn't take too long to be answered but I simply can't find anything using a google search. It's more of a problem from number theory rather than a physical one. I am referring to the Wikipedia article to Shor's algorithm and I still can't get my head around how the...

Hello What is the standard definition of a polynomial? according to the book I am using a polynomial is an algebraic expression which is integral and rational for all the terms. It gives no definition of integral or rational seperately, but I think integral means that the variables are to...

Homework Statement The image of a linear transformation = columnspace of the matrix associated to the linear transformation. More specifically though, given the transformation from Rn to Rm: from subspace X to subspace Y, the image of a linear transformation is equal to the set of vectors in X...

Hello, in group theory a regular action on a G-set S is such that for every x,y∈S, there exists exactly one g such that g⋅x = y. I noticed however that in the theory of Lie groups the definition of regular action is quite different (see Definition 1.4.8 at this link). Is there a connection...

Homework Statement I have a question about isomorphisms -- I'm not sure if this is the right forum to post this in though. A linear transformation is an isomorphism if the matrix associated to the transformation is invertable. This means that if the determinant of a transformation matrix = 0...

what is the definition of phase lag and phase difference in waves and how are these 2 related?please explain in simple words and with real life examples. Please explain phase,phase lag and phase difference from scratch.

In the derivation of the Clausius inequality, T is the temperature of the reservoir at that point in the cycle, but in the definition of entropy it becomes the temperature of the system. This seems to work for a Carnot cycle, where the two are the same, but for other processes, such as an object...

Definition: If $S$ and $T$ are nonempty sets then a mapping from $S$ to $T$ is a subset, $M$, of $S \times T$ such that for every $s \in S$ there's a unique $t \in T$ such that the ordered pair $(s, t) \in M.$ Could someone please explain how these are mappings. The notation of the definition...

Hello, In my Real Analysis textbook (Schramm) they say that an example of compound statement would be "Either 1+1=2 or a pencil is a useful tool in neurosurgery." I was wondering why this isn't a non-statement since I don't see where the truth value of it would be. Thanks!

hi, i'm student in a university. I do not understand the definition of these concepts, and I would like to know the properties of these and it depends questions like They depend on the material used? the atomic number? thanks for answering capisko,

I have been playing around with calculus for a while and I wondered what would it be like to make some changes to the definition of derivatives. I'd like to look at the original definition of derivatives in this way (everything is in lim Δx→0): F(x+Δx) - F(x) = F'(x) * Δx The Δx factor...

A lot of web pages/books show how to use cosx=sin(Pi/2-x) and the chain rule to prove that the derivative of cosx=-sinx. My question is how to use this identity and the defintion of the derivative to prove the same thing. Or whether it is at all possible. Seeing that i get...

Why is it that a vector can be described in terms of a simple linear combination, like v = xi + yj + zk, where v is a vector, and i, j, and k are all unit vectors. It just seems a bit convenient that it's as simple as just adding the components this way. It seems like there should be a bit more...

When CLAS of Jlab describe the result of the process ep→epπ,the use the terminal "transverse amplitude" Ml±(W,Q2), El±(W,Q2),and "scalar(longitudinal) amplitudes"Sl±(W,Q2),they correspond to photons of the magnetic, electric, and Coulombic type.Are they observables? The index of...

I am using Spivak calculus. The reason why epsilon-delta definition works is for every ε>0, we can find some δ>0 for which definition of limit holds. Spivak asserts yhat if we can find a δ>0 for every ε>0, then we can find some δ1 if ε equals ε/2. How is this statement possible? Since ε>0, then...

As I'm seeing things, there are these choices for a definition of relativistic phase velocity u; a) u = (mc^2)/ p b) u = E / p Now I like choice a) because it leads to a correct-looking index of refraction via n = c / u. It leads to a correct-looking solution to the ray equation. However...

Hi All, Hope this is not too simple/dumb. I think I have a good idea of what an inner join of two SQL tables T1, T2 along a common field F is, but , for an exercise, I am looking for a precise definition. I am looking for a definition of this sort: (please correct if necessary or let me know if...

In his book, Euler gives the definition of a variable to be : "A variable quantity is an indeterminate or universal quantity, which includes within itself all completely determined values." What does he mean exactly in the last part of the sentence?

Why we can not define a vector as a quantity which has magnitude and direction? Why we define the vectors according to behavior of its components in rotated coordinate-frames?

Multiple_Authors submitted a new PF Insights post Building a Definition for Heat Continue reading the Original PF Insights Post.

Homework Statement Let A be the area of the region that lies under the graph of f(x) = 2x 2 + 5 between x = 0 and x = 4. Find an expression for A using n rectangles. Then evaluate this expression. Homework Equations Answer is 188/3 h= (4/n) The Attempt at a Solution [/B] The problem I am...

We talk about local effects and surfaces being "in contact" with one another but do we have a vigorous definition for such a state? The objects reach a distance where their repelling EM charges resist and balance against a given force (such as gravitation)...but increased charges would make...

Hi All, My apologies, I think I may have asked this question already, but I could not find it. Here it goes: I have seen the usage of the word 'relation', specifically a relation between tables but I have not seen a formal definition. From what I understand, tables X,Y are related to each other...

Is the principle square root just the positive and negative roots of any number (as opposed to just the positive)? I've seen some confusing definitions of this term online and thought I'd double-check with knowledgeable math people here. Lastly, if it is just the + and - roots of any number...

I am struggling to properly understand the \varepsilon-\delta definition of limits. So, f(x) gets closer to L as x approaches a. That is okay. However, taking the leap from there to the \varepsilon-\delta definition is something I have never really been able to do. Why is the formulation we...

In the propagation of non-monochromatic waves, the group velocity is defined as v_g = \displaystyle \frac{d \omega}{d k} It seems here that \omega is considered a function of k and not viceversa. But in the presence of a signal source, like an antenna in the case of electro-magnetic wave or a...

The first Friedmann equation for a flat Universe is given by: $$\bigg(\frac{\dot{a}(t)}{a(t)}\bigg)^2 = \frac{8 \pi G}{3} \rho(t)$$ The energy density ##\rho(t)## is given by: $$\rho(t) \propto \frac{E(t)}{a(t)^3}$$ where ##E(t)## is the energy of the cosmological fluid in a co-moving...