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1:11 AM
::tumbleweeds::
 
user228700
2:02 AM
Hi everyone :-)
 
user218912
@0celo7 guess what
 
no
 
user218912
:(
 
well are you gonna tell me
 
user218912
well turns out you're not supposed to calculate the integral except for limiting cases.
 
user218912
2:14 AM
another occurrence of me being dumb and not reading the question properly.
 
I read the question
I figured you had to go as far as possible with the integral
 
user218912
also the inner integral with the $d^3x$ is a delta function
 
I don't remember the integral
 
Howdy
 
user218912
hi
 
2:58 AM
Hi, everybody.
 
hello @DanielSank
 
3:23 AM
@0celo7 'sup, bro?
 
the frame bundle
 
::nods::
True, dat.
 
trying to understand how Riemann curvature determines the curvature form in the frame bundle, specifically.
 
user116211
4:07 AM
Ahhhh... an early homework problem in elasticity. I didn't ask you to do my homework, please don't ask me to do yours. — Jon Custer 4 hours ago
 
user116211
Jon is witty sometimes ;)
 
4:58 AM
Just typed up a very detailed analysis of the vibrating string.
@0celo7 there are typos in what I wrote.
Dang.
 
Why @ me, @DanielSank ?
 
I dunno. I figured you'd find more typos.
Also, you're here.
 
I'm currently trying to understand why anyone would define a space to be separable.
 
Hm?
 
old geometry books use weird definitions of manifolds
the modern one wasn't formalized until like the 70s it seems
this book defines them to be separable
and I can't see why one would do that
 
5:04 AM
Manifold: Thing that's locally like $\mathbb{R}^n$?
 
The modern definition is a locally Euclidean Hausdorff space with countable base.
but one can replace "countable base" with many things
they're all equivalent, and take varying amounts of effort to show
 
@0celo7 Is that to avoid things like $L^2$?
 
$L^2$?
The usual pathological example is the long line.
 
@0celo7 Set of square integrable functions.
 
$L^2$ is a Banach space.
That's a manifold in a more general sense.
 
5:07 AM
It's doesn't have a countable basis though.
 
@DanielSank Maybe, but it's not locally Euclidean either.
 
@0celo7 I don't even know what that means, lol.
 
@DanielSank No open set of $L^2$ is homeomorphic to $\Bbb R^n$.
@DanielSank In any case, what you want is to prevent manifolds from being "too large."
 
@0celo7 Да.
 
Some people require just paracompactness, which is weaker.
Then something like $\Bbb R$ copies of $\Bbb R$ would be a manifold.
 
5:10 AM
@0celo7 o_O
 
@DanielSank Right.
 
@0celo7 Is that not called $\mathbb{R}^2$?
Hm, perhaps not.
 
But then they trick you and define them to be connected, which is stronger than second countability.
@DanielSank No, that's $\Bbb R\times\Bbb R$.
I'm talking about $\Bbb R^\Bbb R$.
wayyyyyy bigger
 
I don't even know how to think about that.
I also don't know why you don't like linear algebra more.
 
I wonder if $\Bbb R^\omega$ is a manifold.
 
5:12 AM
You can use it to understand stuff.
 
Depends on what topology you use.
If you use the product topology it's metrizable.
Hence paracompact.
So probably a manifold, but maybe not second countable.
@DanielSank It's too hard.
 
user228700
Hello :-)
 
Hi @Kaumudi.
 
hi
 
6:03 AM
@vzn Sorry, for many reasons I prefer to decline your invitation. Bye, Valter
 
user116211
@ValterMoretti You don't have to bother; we respect your schedule; thanks for responding.
 
user228700
@JohnRennie: Hi :-) Are u there?
 
Morning, yes I'm here though I have a job to do in 15 minutes.
 
user228700
Oh, crap. OK, small question?
 
user228700
Or later..?
 
6:16 AM
Go ahead ...
 
user228700
OK, so I've been trying to think about tension as a force that arises when there is some constraint on the body and then, I came across this problem:
 
user228700
 
OK, that looks easy ...
What bits of the question are being troublesome?
 
user228700
Standing inside the elevator after the cable has broken, how to figure out what the constraint on the block is? It has its weight acting downward and since our frame isn't inertial, we introduce a pseudo force and now it looks like the block is just floating around. Sure, the spring is connected to it, but why is that tension there? What constraint is the block trying to break? It's just float around, right..?
 
An object in free fall behaves the same as an object in zero gravity
So once the elevator cable breaks the mass and spring behave as if they were floating in space
 
user228700
6:22 AM
Yeas, OK...
 
user228700
*floating around
 
Before the cable breaks the mass is pulled down by a force $F=mg$, and this extends the spring by $x = mg/k$.
OK so far?
 
user228700
OK...
 
So once the cable breaks we have, in effect, a mass on a spring that's been stretched by $x=k/mg$ floating in space. The spring wants to return to its equilibrium length, so it exerts a force on the mass and the system starts oscilalting.
The only (conceptually) hard bit of the problem is realising that once the cable breaks the system behaves like it's floating in space.
In fact this is one of the basic principles in general relativity
 
user228700
OK, that makes sense, but I was wondering why that tension is still there..? Maybe I'm coming at this the wrong way, but ever since we had that discussion about why tension starts acting, I've been thinking about tension as a force that tries to stop a body from moving a certain way because of other forces but in this case, since the body doesn't want to go anywhere, why won't that tension cease to exist?
 
user228700
6:29 AM
Oh, wait, hang on.
 
user228700
Okay, I got it.
 
user228700
"The spring wants to return to its equilibrium length, so it exerts a force on the mass and the system starts oscilalting."
 
user228700
This makes sense.
 
user228700
Okay, tension is super weird.
 
user228700
Anyway, OK, I think I got it :-) Thanks, guru! _/_
 
6:33 AM
Good timing. I'm busy now for about half an hour ...
 
6:48 AM
Wow, "guru".
Say, that's not a bad title, @JohnRennie.
 
@DanielSank $\mathbb{R}^{\mathbb{R}} $ is the set of all functions from the reals to the reals ;-)
The exponential notation for the set of functions is pretty enlightening (as well as true)
 
Sigh ...
0
Q: Did Joseph Priestley propose QFT?

anonymouswhoIn the 18th century, Joseph Priestley wrote a book called Disquisitions relating to Matter and Spirit, in which he says: It is maintained in this treatise, that neither matter nor spirit (meaning by the latter the subject of sense and thought) correspond to the definitions above mentioned. Fo...

 
user116211
@JohnRennie WTH is that?
 
user116211
7:03 AM
Hey @DanielSank, you here?
 
@MAFIA36790 yeah
What's up?
 
user116211
@DanielSank Could you tell me what's wrong in my post:
 
user116211
-1
A: When can a force be an Impulsive force?

MAFIA36790As freecharly stated in his post, impulsive force is defined to be the force which acts for an infinitesimally short interval of time and yet is responsible for a finite change in momentum of the system on which the impulsive force is applied. As implied from Newton's Second Law of Motion, impul...

 
user116211
?
 
@yuggib I wasn't quick enough to click the link you sent me a couple of days ago. Could you please send it again?
 
7:11 AM
@MAFIA36790 A lot of the math and wording is wrong/confusing.
Editing...
Uh, actually I'm not sure how to edit.
 
user116211
@DanielSank Thanks.
 
user116211
ohh, okay.
 
The post mentions the delta function out of nowhere, and just doesn't connection the ideas...
 
user116211
@DanielSank Because the impulsive force is zero everywhere except at a certain point where practically it is infinite; the spike graph of $\delta\,?$
 
@MAFIA36790 Yes but what you wrote doesn't say that.
Read it back to yourself.
It just doesn't make sense.
And there's unnecessary bold etc.
 
user116211
7:15 AM
@DanielSank I did mention:
 
user116211
> The whole point of defining the impulsive force by $\delta$ is that $\bf F$ is practically infinite in $t= \tau$ and is zero everywhere.
 
user116211
Okay, @DanielSank, could you tell me how to modify the post?
 
@MAFIA36790 This part: "; it is non-zero "only very near" $\tau$ in $(\tau - \epsilon/2, \tau + \epsilon/2)$ and zero everywhere."
 
user116211
@DanielSank Should I remove it?
 
Slow down.
Here are the problems:
1) $\tau$ came out of nowhere.
2) Why is the word "is" in italics?
3) What does "...and zero everywhere" mean?
4) Why is "everywhere" in bold?
5) In equation Ia, you've written $$\Delta p = \int_{\tau - \epsilon/2}^{\tau+\epsilon/2} \mathbf{F}(\tau) dt$$
but it should be $\mathbf{F}(t)$.
 
user116211
7:28 AM
@DanielSank Okay, that's a typo.
 
6) Before all this, you say "...an infinitesimally short time interval $|\Delta t| < \epsilon$. That's not what you mean. You mean $|t - \tau| < \epsilon/2$.
Furthermore, you never expand on the notion of infinitesimal. It would be better to be honest that $\epsilon$ is a positive number and explain that a force is impulsive if $\epsilon$ is smaller than other time scales you care about.
 
user116211
@DanielSank That's the point of $\delta,$ isn't it? It's zero everywhere except at the point, $\tau\,.$
 
In other words, don't say "infinitesimal", a complex and actually not well defined word, and then not use it! Instead, use simple language and explain what's going on clearly.
@MAFIA36790 yes, but you didn't make that link. It's in your head but not in the post.
 
user116211
@DanielSank Well, in $|\Delta t|\lt \epsilon$ is different $\epsilon\,.$ Okay, I'm seeing the confusions and the flaws.
 
user228700
@JohnRennie: I was wondering...how come so many British girls' names end with the sound "ie"? Brady, Dodie, Hedy. What the heck is up with that? (And I say British girls because those are the only kind I've come across. )
 
7:32 AM
@Kaumudi Interesting. I've never met anyone with those names.
 
user228700
I haven't met them per se. YouTube.
 
However, I know one person who's name does end in the "ee" sound... Kaumudi!
 
^ i.e. nickname
 
user228700
@JohnRennie No, but all these are their real names!
 
user116211
7:33 AM
Stay tuned, @Daniel; I'm editing....
 
user228700
@DanielSank :-P I wonder if u're pronouncing it right tho.
 
@Kaumudi Most assuredly not.
 
user228700
@DanielSank :-P It's cow-moo(lol)-thee.
 
@Kaumudi What happens is we start with they original form of the name, e.g. Jonathan, and it gets modified to the diminutive form Johnny. Then over time parents who aren't philologists don't realise it's a diminutive form and name their child Johnny.
 
user228700
@JohnRennie Riight.
 
7:36 AM
So now I suppose the question is what is the diminutive of Johnny? :-)
 
user228700
:-P Johnny's a pretty small word.
 
@Kaumudi Oh, that's how I would have said it.
The "d" is like "th" is many languages.
 
@Kaumudi is the name Gandhiji a diminutive in the same way? Or does its construction come from a different source?
 
@JohnRennie Russian diminutives are some times hilariously longer than the originals.
Anna --> Annochka
 
I don't think that's uncommon. eg in German you add chen and that can make the diminutive form longer than the original.
 
7:44 AM
@JohnRennie It's not uncommon. It's just funny.
 
user116211
@DanielSank: What about this "$\tau$ is the instant when the force is practically non-zero" or "$\tau$ is the instant when the impulse occurs"?
 
"instance" -> "instant"
 
user116211
@DanielSank yes, yes; oops.
 
user116211
8:01 AM
@DanielSank: Done! Could you check that now?
 
user228700
8:14 AM
@DanielSank Oh! Well, most of my friends used to pronounce it "d" first, so I have to admit that I'm very surprised!
 
user228700
@JohnRennie No, it's not exactly diminutive. "Ji" is strung at the back of the names of people whom we are addressing, whom we respect very much. Eg: some people address their mothers by maji(ma(mother)+ji).
 
Aha, an honorific rather than a diminutive.
 
user228700
@JohnRennie Teaching me something new everyday! :-D
 
user116211
@user104372, you are here?
 
user116211
Hmm, I knew impulsive force to be acting for an infinitesimally small amount of time.
 
user116211
8:27 AM
@user104372, It is written in my book; it's a pretty common application to model impulsive force with dirac delta function after introducing it.
 
user228700
@JohnRennie: Quick question about statistics. Can u help please?
 
I'll try, though my knowledge of stats is rather basic
 
user228700
OK.
 
user116211
Go on; I'm minoring in stats.
 
user228700
:-P This is a really trivial question. This:
 
user116211
8:36 AM
@JohnRennie; could you clarify what impulsive force actually is? Isn't it the force acting over a very infinitesimally short interval of time?
 
user228700
 
impulsive force is a meaningless term
 
user116211
._.
 
user116211
@Kaumudi What's the question?
 
user228700
What have they done in that second step?! :o
 
user116211
8:38 AM
@Kaumudi Apply $(a+b)^2$ and go on...
 
user228700
Uh...but it doesn't add up :/
 
user228700
Tried that first but where are the other terms..?
 
I'd have to get a piece of paper and do the algebra, but remember that $\bar{x} = \frac{\sum x}{n}$
 
user116211
@Kaumudi Your book is in mess.
 
user228700
@JohnRennie OK! Arrived at that. Seems that my brain is a little lazy today huh :/
 
user228700
8:42 AM
@MAFIA36790 Uh, why do u say this..?
 
user116211
@Kaumudi Because it just jot down the result without deriving anything.
 
user228700
@MAFIA36790 Yeah, that's what they do every time. Stupid book, but at least I get to learn a lot this way.
 
user116211
@Kaumudi Wait... I'm showing you the derivation...
 
user228700
@MAFIA36790 No, don't bother! I got it, thanks :-)
 
@Kaumudi: the working is done here:
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean, and it informally measures how far a set of (random) numbers are spread out from their mean. The variance has a central role in statistics. It is used in descriptive statistics, statistical inference, hypothesis testing, goodness of fit, Monte Carlo sampling, amongst many others. This makes it a central quantity in numerous fields such as physics, biology, chemistry, economics, and finance. The variance is the square of the standard deviation, the second central moment...
 
user228700
8:46 AM
@JohnRennie (Y) Thanks!
 
user116211
$$\begin{align}\sigma^ 2 &=\mathrm E (X-\overline X)^2\\ &=\mathrm E\left(X^2 -2X\overline X + \overline X^2 \right) \\ &= \mathrm E(X^2) -2\overline X~\mathrm E(X) + \overline X^2\\ &= \mathrm E(X^2)- \{\mathrm E(X)\}^2\end{align}$$
 
user228700
@MAFIA36790 Yeah, was able to arrive at that on my own. Thanks for the effort :-)
 
user116211
@Kaumudi I was in the middle of the writing; so I posted it up $\uparrow\,.$
 
user228700
OK, thanks again :-)
 
user116211
@user104372; Your post is totally right now; +1.
 
user228700
8:50 AM
Wait, can u tell me what the heck $\sigma_d$ is..? (As given in my textbook)
 
user116211
@Kaumudi They have shifted the origin.
 
user228700
@MAFIA36790 To make the calculations less cumbersome?
 
user116211
@Kaumudi yes.
 
user228700
OK, how do we adjust for this change in the final value..?
 
user116211
@Kaumudi Variance doesn't get altered by shifting of the origin.
 
user228700
8:54 AM
@MAFIA36790 Ohh, right...
 
user228700
OK, thanks!
 
9:16 AM
Good grief! He's at it again :-(
-1
Q: Can Planck's constant be defined through the speed of light

JokelaTurbineThis paper of mine claims so; ABSTRACT; In this Paper, I develop the idea of massless physics further. I find the atom diameter through Boltzmann constant and gas-theory. I test its universality with the observations from other planets. Supported by these observations, I conclude that molec...

 
user116211
> This paper of mine claims so
 
9:32 AM
[Division by zero] After some fiddling, got an interesting rock paper scissors like system where a absorbs b, b absorbs c and c absorbs a in the + cayley table. However I need to check the definition of a zero element again to see whether there are actually zero elements in this system.
The system is associative in + for only 9 out of all the possible 27 cases. Distributive law is checked to worked fine by running through all 27 possibilities.
The system can be easily made into an infinite cycle by "disengaging" one of the operations in the $\times$ cayley table so that it unravels
 
user116211
@MAFIA36790 It's like the thief says his hands stole and only his hands should be punished and not him ;P
 
Anyone know Sakharov's conditions? Why is out of thermal equilibrium required?
 
10:02 AM
Fine, not a zero element...
[Division by zero]
a(b+c)=ab+ac
(b+c)a=ba+ca
Add axiom y+x=x+y
ba+ca=ca+ba
*Initiate breakage of + commutativity*
*Recomputing new algebraic structure in progress*
*Warning: DO NOT absorb 0*
 
user116211
10:13 AM
@Secret Ring product is always distributive over ring addition.
 
JiK
11:35 AM
A question I saw in SE got me thinking about this again: The average speed is naturally defined as displacement/time, so it is $\int_0^T v(t) dt / T$. So it's the weighted average of velocities of short segments weighted by time. A while ago a friend of mine said he wants to mislead people by telling his average speed over a bike trip weighted by distance, not time, to get bigger numbers. He asked what should he call it because it's not "average speed".
So the number would be $\int_0^S v(s) ds /S = \int_0^T v(t)^2 dt / S = \int_0^T v(t)^2 dt / T / v_{avg}$. I couldn't think of any way this would be useful in any physics so I couldn't give him a word for that. But it got me curious; does by chance this happen to be useful anywhere?
 
@MAFIA36790 Yup, I have no problems with that
 
 
1 hour later…
user116211
1:02 PM
@Secret I'm just saying it was implied.
 
user116211
1:37 PM
What to do with this:
 
user116211
0
Q: Could the machine described by this patent work?

Nicole JudgeA friend has shown me this, and I'm quite interested 1) why this is an official patent if it wouldn't work 2) and if it would work, why isn't it already created? https://www.google.com/patents/US20060071122

 
user116211
My hands are really tempted to vote to close it on..... on what reason? it's not mainstream physics? hmm.
 
user116211
Anyways, I'm leaving it for the community to decide.
 
user116211
Let me sneak into Lumo's blog...
 
user116211
@yuggib o/
 
@MAFIA36790 \o
 
@JohnRennie Should I remove this post? I have no need to disturb anone.
 
user116211
@JokelaTurbine; You shouldn't. Opinions vary but that doesn't mean you have to delete your post.
 
user116211
However, I will say we are not reviewers; SE is not for personal theories or for reviewing papers that are not peer-reviewed.
 
user116211
1:54 PM
Phys.SE only deals with mainstream physics; well you know that....
 
Well, I do realize that such stuff is not quite acceptable, and I even understand why. I also don't try to be "smart" and hide the fact that it's only my own thoughts
 
user116211
@yuggib; you must know about Lagrange's method of extremising a definite integral...
 
@MAFIA36790 Yes. That's why I won't be too disturbed to delete it. I am just out of "circles" and dont have any peer reviewing possibilities. + my language my problems.
I actually came here to chat to ask If should delete and rewrite the whole question to better fit the concept. I allready made a change to this direction. and btw, thanks for your edit Mafia36790
 
user116211
I've read Lanczos where he talks about finding the stationary value of $I = \displaystyle\int_a^b F(y, y^\prime, x)~\mathrm dx\,.$
 
user116211
He needs to find $y = f(x)$ which makes the integral stationary.
 
2:02 PM
In mathematics it goes under the name of calculus of variations
 
ugh
I flagged this as off topic, hoping it would go to the queue, but mod close flags autoclose too
-1
Q: Brayton Cycle: challenging thermodynamics problem

Nikita JerschowA brayton cycle is a cycle used in jet engines and can be described as follows: the cycle begins with adiabatic compression from (p1, v1) to (p2,v2), followed by isobaric expansion to (p2,v3). After this, the cycle goes through adiabatic expansion to (p1, v4), until finally returning to (p,1,v1) ...

 
user116211
@yuggib yes, this is the chapter I'm reading.
 
Is there a reason to reopen it?
 
user116211
@ManishEarth Not at all.
 
I could swear that when the close system changed a few years ago they made mod close flags nonbinding
reclosing then
I don't like unanimously closing things, thanks for the +1
 
user116211
2:04 PM
Anyways, then he chooses a "slightly modified function" $y = \overline{f(x)}\,.$
 
user116211
This can be expressed as $$\overline{f(x)} = f(x) + \epsilon ~\phi(x)$$
 
user116211
where $\phi(x)$ is some arbitrary function which satisfies general continuity conditions.
 
user116211
He then tells that he wants to restrict $f(x)$ by the further condition that $f^{\prime\prime}$ exists.
 
user116211
Throughout the range.
 
user116211
However, he added:
 
user116211
2:09 PM
> A similar assumption for $\phi(x)$ is not required.
 
user116211
@yuggib, Could you tell why he said so $\uparrow$?
 
user116211
Well, I'm reading to see whether he mentions any more details on it...
 
2:46 PM
Ok, so now my question is on hold. and I allready edited once. In my point of view this should be within these limits; meta.physics.stackexchange.com/questions/4538/… "For example, a question that proposes a new concept or paradigm, but asks for evaluation of that concept within the framework of current (mainstream) physics is OK."
So should I edit it (how) or delete it?
@JohnRennie -Thank you for answer in advance.
@innisfree pls. define "some rules" more accurately. -thanks.
 
> that the differene between kinetic gas and condensated matter might be the particle's ability to exchange photons.
interesting
I need this
 
@0celo7 You are propably writing to me? Yes. I found it too interesting. And I have been away for a while and developed this further alone. Now I think this is pretty advanced. But it is, and will remain "not-mainstream".
and the rules are; "but asks for evaluation of that concept within the framework of current (mainstream) physics is OK."
 
user218912
3:45 PM
hi
 
*Breaking right multiplicative identity*
*Breaking left or right, additive identities and additive inverses*
*Reconstructing new algebraic structure in progress*
 
user218912
where is ACM :(
 
dead, probably.
 
user116211
He is spending here less time :(
 
user116211
If he becomes mod, then....
 
user116211
3:55 PM
Well, he assured though he would spend the same time ;/
 
4:12 PM
@ManishEarth Yeah, unanimous closing seems kind of not what one would usually want.
 
@DanielSank right, it was an accident
 
Oh, I wasn't commenting on anything you did, just expressing a general opinion.
 
I thought it should be closed, but I can't close it without modhammering it, so I thought I'd flag it so that it goes into the queue. That .. didn't work, because flags still modhammer things :p
ah
 
Mods should have the option for non-binding votes.
 
yeah
 
4:13 PM
I think there's a post on the meta about this, but it's marked "won't do" or whatever.
 
that's been a very long-standing feature request
 
user116211
0
Q: INFRA RAYS CAN'T REACH TO EARTH THROUGH ATMOSHPHERE

Izzaki Ningombam ChesterWhy infra rays can't reach to our earth?why it can't pass through atmosphere?

 
user116211
So beautiful.
 
~Sigh~
Why do people come here, see all of the titles in normal case, and then still decide to all-caps their title?
Fixed.
 
user116211
I was editing...
 
4:19 PM
sorry
 
user116211
np.
 
user116211
Anyways, @DanielSank, I have edited my post earlier of which you marked the flaws; if you have time, please check the edited post.
 
@MAFIA36790 Link?
 
user116211
@DanielSank Here.
 
@MAFIA36790 progress in Bredon?
 
user228700
4:23 PM
Hello y'all! :-)
 
@MAFIA36790 Define $\mathcal{F}$.
 
user116211
@0celo7 Yes, got the book. But haven't read it.
 
Actually, I think you should write $\mathbf{F}(0)$ instead.
Introducing an extra symbol is not needed.
 
user116211
@DanielSank $0$?
 
do it now, should not take you long
@MAFIA36790 $t=0$
 
user116211
4:25 PM
@0celo7 ;(
 
user116211
'I know that.
 
@MAFIA36790 I mean $\mathbf{F}(\tau)$.
 
oh
 
user116211
I asked why it was required.
 
user228700
This is a wonderful website for understanding the world in all its complexity and if you have the time, do check it out (And share it with the people who might benefit!) (BTW, this is not an ad of any sort; just something I thought I'd share here :-))
 
user228700
 
it should be $\tau$
 
Also, note that the dimensions are wrong.
 
#rekt by google AI
 
user116211
@DanielSank Which equation?
 
You have $\Delta p = \mathcal{F}$, which means $\mathcal{F}$ must be a momentum (or impulse, same thing).
That's very confusing notation.
Remember that $\delta(t-\tau)$ has dimensions of $1/[\text{time}]$.
 
user116211
4:26 PM
Okay, I got that.
 
haha, I solved an analysis problem
it was tricky
@MAFIA36790 functional analysis is waiting for you
 
user116211
@0celo7 I'm eagerly waiting....
 
If $(X,d)$ is a compact metric space, any family $\mathscr F\subset C_E^b(X)$ which is equicontinuous at each $x\in X$, is uniformly equicontinuous on $X$.

*Proof*
Let $\epsilon>0$. By equicontinuity, for each $x\in X$ there is a $\delta_x=\delta_x(\epsilon)>0$ such that $B(x,\delta_x)\subset X$ is mapped into $B(f(x),\epsilon/2)\subset E$ by \emph{every} $f\in\mathscr F$. Let $\mathfrak U=\{B(x,\delta_x)\}_{x\in X}$, note that this is an open cover. Hence $\mathfrak U$ has a Lebesgue number $\delta>0$ since $X$ is compact. Suppose $d(x_1,x_2)<\delta$ for some $x_1,x_2\in X$. Then the set
Lebesgue number too OP
Interesting.
I proved a stronger statement than what was needed actually.
 
user116211
@DanielSank: " where $\mathcal F$ has units of force-time."
 
@MAFIA36790 Dude, that's called "impulse" or "momentum".
:D
 
4:39 PM
lol
 
user116211
I surrender T__T
 
@MAFIA36790 Surrender to who?
 
user116211
Nevertheless, thanks @DanielSank for pointing out in details all the flaws; that made the post better than the first one :)
 
@MAFIA36790 Sure.
I appreciate your interest to improve the post.
 
user116211
I need to get back to Lanczos.
 
4:42 PM
Dude, read bredon
 
user116211
I need to complete the Calculus of Variations and d'Alembert's Principle before anything else.
 
user116211
@0celo7 Sure, sure; I'm completing all my other topics left in my hand to be studied to start reading Bredon.
 
I have the strange absence of a desire to buy books right now.
I might be ill.
 
user116211
@0celo7 WTH!
 
I think I have all the books I need
 
user116211
4:48 PM
okay.
 
weird
 
user116211
I have many things left to buy. I need money.
 
user116211
Checking for some way to earn money....
 
yes, you need Kobayashi-Nomizu, do Carmo, Lee, Jost, etc.
 
user116211
Books are rotting in my cart.
 
4:49 PM
Wald, Straumann, Hawking Ellis
Helgason, Lee, Lee
LOTS of books to get
@MAFIA36790 Undergrad research?
 
@JohnRennie I think this comment could have been worded in a more constructive way.
 
user116211
@0celo7 there are not any till third year :(
 
@DanielSank sometimes my patience frays. You should have seen the comment I decided not to post to this question.
 
@JohnRennie post it here
@MAFIA36790 that's three Lees btw, I don't think Lee is good enough to get three times ;)
there are actually four Lees
I don't have one of them ;(
 
user116211
I need Jech, Mendelson, Herstein, Lovelock and Rund; finally Bourbaki Algebra to buy.
 
4:53 PM
I'm hoping he'll release a 2nd edition, his other two books have second editions
 
user116211
There are other books too ;/
 
You do not need Jech or Bourbaki Algebra
 
user116211
I need Jech for Set Theory.
 
Why??
 
user116211
I can omit Bourbaki; no haste.
 
user116211
4:54 PM
@0celo7 Because it's lucidly written.
 
Why do you want to learn set theory
 
@JohnRennie If you can't say anything constructive..., right?
 
user116211
@0celo7 Hmm; frankly speaking it's not in our syllabus; but I do want to learn about set theory; that's the thing.
 
@DanielSank you just keep playing the good cop
 
@JohnRennie I'm not "playing" at anything. I think our site needs to do better at helping new users learn to ask better.
I've made speeches about this many times before.
One of my goals in using this site is to find ways to make e.g. the close reasons valuable resources for learning to ask better.
This is why I made that meta post about renaming the homework policy, for example.
 
4:58 PM
@mafia is set theory a deep discipline? i always thought it wasn't that complicated but maybe theres more to it
 
Getting a question closed is discouraging. The best way to offset that feeling is to give the user a very obvious path forward.
 

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