The h Bar

heather

00:01

@0celo7, I am indeed still here.

And prepared for the discussion

0celo7

@heather ok

heather

ok

0celo7

So open intervals

What exactly is special about them?

It's this: given an open interval $I$, and a point $x\in I$, there is another open interval $J$ containing $x$ such that $J\subset I$.

strict subset in this case

we can make $J$ really smal

In fact we can take it of the form $(x-\delta,x+\delta)$ for $\delta<0$ small.

heather

so, for an example, if you have the open interval (0,1) and a point 0.5 $\in$ the interval, then there is another open interval like (0.25,1) which includes 0.5 and it is a subset of the first interval?

So then, if this is the case

0celo7

you can do better

heather

00:15

right

0celo7

let's define the size of an interval

$\ell (a,b)=|b-a|$

\ell

heather

what is $\ell$

0celo7

"length"

we are doing Lebesgue measure btw :)

heather

Lebesque...googling

0celo7

Not really, but this is how you start it

heather

00:16

ah, okay.

so what if we said with the interval (0,1) the point is $\infty - 1$ and then the new interval is ($\infty - 2$, 1)

but then, of course, you have the problem that $\infty - 1 = \infty$...

0celo7

umm, where did infinity come from?

heather

because we are trying to get infinitely close to 1 to define it such that the upper bound of (0,1) is 1, right?

0celo7

Not infinitely close :/

heather

oh :/

Andras Deak

infinitesimally;)

0celo7

00:19

no, not that either

Andras Deak

awwww

0celo7

@heather is $2$ an upper bound for that interval?

heather

Okay, what is the difference between infinitesimally and infinitely close?

Andras Deak

@heather sorry, ignore me now:)

heather

@0celo7, (0,1)? I don't think so...

0celo7

00:19

don't use either of those words

heather

@AndrasDeak, sorry, yeah =)

0celo7

@heather Why not? Everything in that interval is smaller

heather

But it is beyond the interval, right? I mean it has to be in the interval, right?

I mean, if you let it be beyond the interval, then the upper bound of everything is $\infty$

0celo7

No, look back at your definitions

@heather Ok. Don't ever use (i) infinitely (ii) infinitesimally (iii) $\pm\infty$ ever again. Except for in the context $\lim_{n\to\infty}$.

3

heather

@0celo7, ever!? but, but, limits, and things =P

0celo7

00:22

But even then, that notation is probably terrible.

Emilio Pisanty

@heather you can use $\infty$ strictly when it is to the right of a $\to$, but that's it

and it doesn't actually mean anything is infinite

heather

sidebar, you can do \lim_\limits{n\rightarrow\infty} to get the $n\rightarrow\infty$ under the $\lim$

0celo7

$\lim_\limits{n\rightarrow\infty}$

Yeah I know that.

Andras Deak

(you can also have a meaningful $\infty$ on the right hand side of a limit, right?)

0celo7

@AndrasDeak Yes, but let's not confuse her.

Andras Deak

00:24

(hence parentheses)

heather

right and you can do \limits with any operator and stuff, like $\int$

0celo7

@heather Don't do it with integrals.

heather

oh, okay.

0celo7

You want the limits on the side of that.

heather

gotcha

0celo7

00:25

@heather find the definition of "upper bound" in the chat

heather

I'm looking, I searched the wrong thing at first

Andras Deak

I'll help where I can and stop interfering:D Sorry for any confusion, and good night

ACuriousMind

@0celo7 That depends on your typographic convention ;)

heather

2 days ago, by 0celo7

Ok, last thing for today is the least upper bound. A least upper bound for a set, called $\sup A$ (supremum) is a a number such that (i) $\sup A$ is an upper bound for $A$, (ii) if $b$ is an upper bound for $A$, then $\sup A\le b$.

@AndrasDeak, good night =)

2 days ago, by 0celo7

Let $A\subset \Bbb R$, then $b\in\Bbb R$ is an upper bound for $A$ if $b\ge a$ for any $a\in A$.

oh...so it is allowable. but then why isn't the word that shall not be mentioned the upper bound for every set?

0celo7

@ACuriousMind There is one correct way for typing mathematics. The Germans were wrong in the case of integrals, I'm sorry.

@heather There are many upper bounds

Note I said "an" upper bound.

heather

00:30

there are multiple definitions of an upper bound?

0celo7

No, there are multiple upper bounds

@ACuriousMind you're welcome to add anything

heather

rephrasing: every number greater than every $a\in A$ is an upper bound? So there are a word that shall not be mentioned number of upper bounds?

^sorry, last time I'll use word that shall not be mentioned, except here

0celo7

Shit. That's a legitimate use of the word.

Yes, there are infinitely many upper bounds, in general.

heather

Ha! =)

Perhaps I need to backtrack then. Why is the upper bound not more rigorously defined? I don't see the use of having infinitely many upper bounds.

0celo7

How else should it be defined?

it's perfectly "rigorous"

heather

00:33

well I didn't quite mean not rigorous, perhaps more strictly is what I meant. but my definition would be (and I know it is a poor one, but):

Let $A$ be a subset of $\mathbb{R}$, then $b \in A$ is an upper bound for $A$ if $b\geq a$ for any $a \in A$.

0celo7

If $b\in A$, then $(0,1)$ will not have an upper bound by your definition.

heather

yeah, it will, it would be 1, because 0.9 repeating equals 1.

0celo7

0.9 repeating is also banned

@ACuriousMind halp

heather

why? I don't understand what is wrong with a perfectly legitimate number.

0celo7

(0,1) does not contain 1

that's what (0,1) means

heather

00:37

no, but it contains 0.9 repeating

0celo7

No, because that's 1.

ACuriousMind

@heather $0.\bar{9}$ is a legitimate number, but it's not in $(0,1)$.

heather

oh, okay. Then it'd be 0.9999...98 (the upper bound, I mean).

0celo7

That's not a legitimate number

ACuriousMind

By definition, $x\in(0,1)$ means $0 < x < 1$, but since $0.\bar{9} = 1$ it's not smaller than 1

@heather Now that is not a legitimate number

heather

00:39

why not?

i mean, i get it, but i don't.

ACuriousMind

The decimal representation of a real is either finite, infinite and periodic, or infinite and non-repeating. That there is neither of those cases (assuming you meant for the number of 9s in there to be infinite).

heather

well, infinite up until an eight, yes.

0celo7

ahhh

ACuriousMind

@heather What does "infinite up until" mean?

0celo7

BANNED WORD

ACuriousMind

00:41

There is no such thing as the "infinite"th digit of a real

heather

@ACuriousMind, I don't know if I could give a formal definition, but take 0.9 repeating and switch out the last digit with an 8. That is what I mean, though I guess I have to concede that it is not a real number.

@0celo7, sorry, sorry.

0celo7

"Last digit" is not a thing.

heather

darn the banned word

ACuriousMind

@heather Yeah, there's no such thing as the last digit - "repeating" precisely means that the $n$th digit is 9 for all finite values of $n$

heather

okay, okay @0celo7, the upper bound is not defined here. and it isn't for any open interval. but it is better than infinitely many upper bounds =P

0celo7

00:43

BANNED WORD

ACuriousMind

@0celo7 chill

heather

hey, that was a legitimate use, you admitted it

ACuriousMind

@heather do you mean infinitely many upper bounds?

heather

@ACuriousMind, yes, editing

okay, fixed

ACuriousMind

Then the notion of supremum is precisely there to get rid of that annoyance - the supremum is the least upper bound.

heather

00:45

oh...I think everything just clicked.

@0celo7, alright, alright, you are right. I will never ever stray from the path of the Jedi again =P

0celo7

@ACuriousMind Just checking: $A^\circ=\emptyset$ is equivalent to $A$ containing no open sets.

ACuriousMind

@0celo7 yes

heather

@ACuriousMind, I've been pointed at 3 different GR textbooks, and the only other person in hbar at the moment recommended one of said textbooks, would you mind recommending which one is best?

ACuriousMind

@heather I do mind, because I cannot in good faith recommend books I have never read.

heather

@ACuriousMind, okay =) I didn't know if you'd maybe have read some of them.

ACuriousMind

00:50

I'm the worst person to ask for book recommendations because I have never learned a subject by reading a book.

heather

@ACuriousMind, ah, okay.

@0celo7, so then going back to the original problem, 2 would indeed be an upper bound for (0,1)

0celo7

1.5?

heather

?

0celo7

Is 1.5 an upper bound?

heather

yes

0celo7

00:55

is 1 an upper bound?

heather

yes

0celo7

How about anything smaller than 1?

heather

no

0celo7

Why not?

heather

because the upper bound must be greater than every member of the set

and 0.9 repeating equals 1 =P

0celo7

00:57

what is with you and 0.9 repeating

heather

at that point it was just me giving you a hard time =)

but I will not use any of the forbidden words again for now.

0celo7

I will post a proof, and you should read through it

heather

that makes sense

huh. it reminds me of limits.

0celo7

01:17

Slightly gross but I had an analysis eureka on the toilet :)

heather

oh, gosh.

the analysis eureka? great!

the toilet part? just no.

0celo7

@heather Well I solved two homework problems :)

heather

@0celo7, that's good.

Okay, I know you recommended Hawking and Ellis. But seriously, I got recommended the following three textbooks:

amazon.com/Spacetime-Geometry-Introduction-General-Relativity/…

amazon.com/…

And I'm really not sure which one I should go for. I've gotten strong recommendations for all of them.

0celo7

1 and 3 were troll recommendations

heather

Seriously? Oh, okay. #1 was suggested by Jim

0celo7

01:32

1 is graduate level and 3 is extremely hard, even for researchers in geometry and analysis

heather

which is why I'm surprised by that. but thank you.

0celo7

Ok, not a troll

But you're not going to do well with it at all

ACuriousMind

@0celo7 I don't think 1 wasn't serious, why do you think so?

heather

oh...yeah, maybe not then =P

0celo7

@ACuriousMind She will not understand Carroll.

heather

01:33

I probably will not if it is graduate level.

0celo7

@heather Definitely do not get #3 yet

heather

@0celo7, okay, I definitely can believe that

ACuriousMind

@0celo7 Yes, Jim also said that.

0celo7

My long-term goal for college is to understand chapters >=7

But it's hard :(

ACuriousMind

But the recommendation as an intro to GR was still serious, I believe, he was just recommending waiting until she can understand Carroll.

0celo7

01:34

Need to learn Sobolev spaces

@ACuriousMind There are easier books

Like Zee, of course

heather

Zee...hmm, googling

oh, that looks good as well. now I'm in another dilemma, but it is a two book dilemma instead of a three book dilemma. progress =)

0celo7

Zee is actually physics

Very math light

But you will learn life lessons from it

heather

life lessons are good

@0celo7, what sorts of life lessons?

0celo7

don't calculate before you know the answer

shut up and calculate

Lagrangian mechanics

some history

an amusing story with a fly and a camcorder

heather

@0celo7, sounds cool. So, in the final analysis: Callahan or Zee?

^no pun intended

0celo7

01:47

Zee is what I recommend. it was my first

heather

Okay. I will put that one on my list, because I am trusting that you are not trolling. =P

0celo7

I'm not

ask @ACuriousMind

I'm 100% serious about Zee

Mike Miller

he's right

he's still a troll though

ACuriousMind

He is serious, his love for Zee is true

0celo7

@MikeMiller Huh?

heather

01:50

@0celo7, oh, come on, you've admitted it infinitely many times <- and yes I said infinity on purpose

0celo7

Sometimes I kid, but I'm certainly not a "troll"

ACuriousMind

11 hours ago, by 0celo7

@ACuriousMind Sometimes my personality randomly splits (pair production) and trolls. I can't help it

11 hours ago, by 0celo7

@ACuriousMind I'm sorry. I was trolling subconsciously.

0celo7

I thought you were my friend

heather

@0celo7, you are a special kind of troll, that is not bad, just hilarious

0celo7

Thanks?

ACuriousMind

01:53

There's a lot more where those came from :P

user218912

hiii

0celo7

I just spent 10 minutes proving $|\cdot|$ is continuous. Maybe I need some sleep? But it's onl 10

heather

@obe, hello

user218912

another day spent doing nothing productive.

heather

@0celo7, thank you for the analysis lesson, the GR book help, and other stuff

adios all

0celo7

01:58

@ACuriousMind how can I make my memory better?

ACuriousMind

I have no idea, I never trained remembering things. I do know there are supposedly techniques for that, though

user218912

eat blueberries

0celo7

proof?

I ate lots in high school :o

And we all know my memory was better back then

user218912

there's your proof

user218912

also eat fish and walnuts apparently

user218912

02:01

and exercise often

0celo7

I eat lots of fish

@obe welp

I hate walnuts

user218912

they're ok

user218912

oh and sleep, the most important factor

0celo7

I get 5 hours

user218912

isn't 9 hours recommended lol?

user218912

02:02

5 HOURS?!

user218912

daily?

user218912

I can survive on 7 but days when I get < 5 hours I'm a zombie and sleep in class.

ACuriousMind

People cope very differently with lack of sleep, but 5 hours does sound a bit on the low side if it's consistently that little.

0celo7

Kidding

I get 7, sometimes 8

in HS I got 6...

user218912

lol

user218912

02:05

I get 10 now.

user218912

maybe up to 13...

0celo7

jesus

user218912

that's on days when I don't have qft.

user218912

since qft is a 9am lecture...

user218912

it's actually quite alright because I sleep at like 3am so on days with an early lecture I get like 5 hours of sleep so I make up for it on days with no early lecture.

0celo7

02:29

@obe I think I just physics proofed something

I'm scared

user116211

04:03

@0celo7 The moment you do such things, a step you go back from being a mathematician.

user116211

Anyways,

user116211

0

Q: I have a list of separation vectors, how can I calculate the location vectors?

I need to calculate some location vectors which from separation vectors which are generated from the formula (Ri+1) - (Ri). Ri being a location vector A little background: I have some monomers where I have their separation vectors, but what I want to get is the monomer locations. How can I do t...

vectors

user116211

What is that? I'm not accustomed to any of these terms; homework? For me, it's unclear what he is asking.

dmckee

04:20

Rigid bodies are often defined by saying that there is a set of fixed lengths between the particles that make them up or between geometrically distinct features of the form.

Add some information about orientation and now you have vectors between various parts of an object. In principle know the orientation and the location of one part in some coordinate system is enough to know the location of all the parts in that coordinate system.

He wants to know how to perform that calculation. Which is as simple as adding vectors.

user228700

Hi everyone :-)

John Rennie

Morning

Anonymous

05:42

meta.physics.stackexchange.com/questions/9303/… Please have a look at the meta post about the new Area 51 proposal. Thank you.

John Rennie

@S007 I've followed this, and I'll add my five sample questions. I think it's a good idea, though I have my doubts about whether there will be enough interest.

Physics Meta

05:59

1

Q: New site proposal specifically for problem solving in Physics on Area 51

"Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics." At present Physics Stack Exchange is more inclined towards answering specific conceptual questions in Physics and not really meant for problem solving at the High School/Undergraduat...

discussion support

user116211

@S007 You have to make it explicitly clear why this proposal is different from several others proposed in Area 51 in the past.

user116211

Let me see how the Physics Overflow crew react to this proposal.

user116211

@johnR, I would also love to hear your concerns and thinkings on this; since you were inclined earlier also to make such platform.

John Rennie

@MAFIA36790 I think there is a place for questions on doing problems. I've run into this myself when trying to do exercises from GR books. Not all authors provide the solutions. The problem will be distinguishing people who really want to learn from people who are just lazy.

I don't think there are any similar Area 51 proposals that are open at the moment. Previous attempts failed because no-one was interested. I fear the same will happen to this proposal. However I feel it's worth a try.

Anonymous

@JohnRennie Thank you for the support. I do not think it will be very difficult to distinguish homework vampires.

Anonymous

06:09

If enough effort is not shown the question will be closed.

Anonymous

We can follow a model similar to Math SE

user116211

Whatever be the fate, just make it sure, the site doesn't turn to Homework-solving service. Work further keeping that in mind.

Anonymous

Also I think we have enough users on Physics SE who want want to support. @MAFIA36790 That's why I am inviting you to add comments in the meta post about what you want it to be

user116211

I will if I have to any; I'm waiting to see the response of the community.

Anonymous

Let us hold a healthy discussion about what it should be and what it should not be in the comments. Ok. As you wish. @MAFIA36790

user116211

06:11

@S007 Math SE is more lenient and somewhat indifferent to homework questions.

user116211

So, I don't think it is good to frame a site based on Math SE.

Anonymous

Well we can negotiate a bit between Physics SE and Math SE

Anonymous

take an average sort of

user116211

sure.

Anonymous

I am sure you faced such problems too during problem solving which could'nt be fitted to Physics SE rules :-). All in all, it should'nt be a homework site but also at the same time we can be a little bit lenient with the rules!

Anonymous

06:14

anyway lets wait and watch

Anonymous

cya

Secret

Make the process a bit more probabilistic, and then you can push harder towards the no cloning limit

DanielSank

@MarkMitchison If you have a minute, please let me know if this answer looks right.

John Rennie

06:30

@S007: OK I've added my five questions

MathJack

@JohnRennie Excellent :-)! I upvoted them. They will be good model questions. Now I just hope some more users support the proposal :-P. Thank you for the help !

DanielSank

Is there a description of that site's scope?

MathJack

@DanielSank See the new meta post please

user116211

@DanielSank That is what I was asking.

user116211

Anyways, @DanielSank o/

DanielSank

06:33

\o

@JohnRennie @MathJack I would like to make a comment about this area 51 proposal.

user116211

Math SE has tons of hint: .... answers.

user116211

Do we want this?

DanielSank

Most of the questions that get closed as homework on this site are closed because they're bad questions, not because they're asking for help solving a problem.

user116211

I don't think so.

John Rennie

@DanielSank I don't think that's true.

user116211

06:35

@DanielSank Not always.

Anonymous

Hint answers may be useful sometimes

user116211

I will have to dig in to give an example.

John Rennie

Have a look at this search

DanielSank

Here is a recent example of a perfectly fine problem solving question.

Anonymous

Btw isnt this the scope Proposed Q&A site for students and physics enthusiasts

DanielSank

06:36

Ok, @JohnRennie, I clicked on the first question in your list.

That's a terrible question and I wouldn't want to frequent a site on which that is a representative question.

Not because it's homework.

user116211

The intention should be clear: it shouldn't be homework solving service; it will help the askers to explain and give insight on the problem solving tactics and how to approach problems under concern.

DanielSank

I don't like it because 1) The author didn't even proof-read the post, and 2) They make absolutely no indication whatsoever about where they're confused.

So I ask you and @MathJack, do you want a site where questions like the one I just linked are representative?

John Rennie

@DanielSank That's a good example of someone who just wants someone else to do their homework for them. That's exactly the sort of question that wouldn't be suitable for the new site.

Anonymous

@DanielSank the question you linked isnt acceptable

Anonymous

it is pure homework

Anonymous

06:39

@JohnRennie thanks for the questions

DanielSank

@S007 @JohnRennie then again I put it to you, what is acceptable on the new site that is not acceptable here?

John Rennie

The site would be aimed at people who are trying to learn physics. Doing exercises is an important part of learning, which is why most textbooks include exercises.

DanielSank

@JohnRennie Indeed, shall I keep going through your list?

@JohnRennie Of course, but you're dodging my question.

We already know that the "homework" policy needs to be renamed. "Homework" is not the issue here.

Anonymous

@DanielSank For example an irodov problem which a person cannot solve but has clearly shown the exact step where he/she is stuck...I hope you are getting the idea

Anonymous

Check my work is not acceptable here on Physics SE

DanielSank

06:41

@S007 That would be acceptable here.

@S007 So "check my work" is one thing acceptable on the new site, but not this one.

Ok.

I will, again, recommend anyone thinking about the "homework" issue to please read this meta post:

26

Q: Should we rename the homework policy?

The homework policy is a constant source of confusion for new (and sometimes established) users. We see this confusion, for example, when users respond to closures based on the homework policy by defending their post with "This is not a homework problem", or similar. Some users have even been con...

discussion tags questions homework

user116211

@DanielSank I didn't get that. Are you saying check my work is acceptable here?

DanielSank

@MAFIA36790 No, check-my-work is not acceptable here.

Anonymous

@DanielSank Yes check-my-work isnt acceptable here but it will be acceptable on the new site provided the user shows considerable effort

Anonymous

The homework policy on Physics SE is a constant debate. Maybe the new site will solve it by diverting problem-solving questions.

Anonymous

did you see the example questions btw?

DanielSank

06:44

@S007 No, it's not in constant debate.

I would argue that in fact most of the recent meta posts about the homework policy barely talked about the homework policy at all.

Anonymous

@DanielSank Well, ok if you say so. But still, this site is not meant for students who are stuck in problem solving

DanielSank

The problem isn't really endless debate so much as a complete lack of focus on actually improving the obvious problems with the present policy. See the meta post linked a few messages up.

NeuroFuzzy

physics GRE is tomorrow! Woohoo

DanielSank

@S007 I strongly disagree. This site is not for terrible questions.

Anonymous

@DanielSank When did I say this site is for terrible questions ?

DanielSank

06:47

@S007 You didn't.

Anonymous

No.

John Rennie

@S007: I suspect it will be hard to raise sufficient interest just from members of this site. The new proposal will need publicising on other sites if it is to have a chance of getting to the beta stage.

DanielSank

@JohnRennie It's hard to get my support because I still don't understand what the proposed scope is.

You might want to clarify that before campaigning.

user116211

@NeuroFuzzy So, should we expect tons of Homework questions these days?

NeuroFuzzy

@MAFIA36790 Heh, maybe right now and the last week, yeah.

Anonymous

06:52

@DanielSank It is for problem solving. For example someone asks "A wide cylindrical vessel 50 cm in height is filled with water and rests on a table. Assuming the viscosity to be negligible, find at what height from the bottom of the vessel a small hole should be perforated for the water jet coming out of it to hit the surface of the table at the maximum distance lmax from the vessel. Find lmax. " .

Anonymous

Then he shows all his steps

Anonymous

And tells us where he is stuck

Anonymous

Is such a question acceptable on Physics SE ?

Anonymous

No.

Anonymous

But it will be allowed on the proposed site.

Anonymous

06:53

I hope you are getting the idea.

Anonymous

I agree we need to solidify the scope

Anonymous

@JohnRennie Can you suggest which on sites I can publicize

Anonymous

?

DanielSank

@S007 I think so. It sounds like you want to allow questions that would be on topic here if the OP were to indicate why they are stuck.

But on the new site, the OP doesn't have to indicate why they are stuck.

That, plus you want to allow check-my-work questions.

user116211

@DanielSank It should have to be defined in the scope of the site, what we actually want; it should have to be made explicitly clear.

DanielSank

06:55

@S007 Quora, and the other physics homework help sites that you can find via Google.

John Rennie

@S007 I'm not sure to be honest. I'm considerably out of touch with where students discuss their problems these days.

Anonymous

@DanielSank You are getting it wrong. Such a question isn't allowed on Physics SE. It is off-topic and homework unless it is about a specific concept.

user116211

The answers won't provide complete solutions; they would just show how to approach the problem from the point where OP is stuck.

Anonymous

@MAFIA36790 exactly

DanielSank

@S007 Could you give an explicit example of a question that would be off topic here, but on-topic on the new site?

Anonymous

06:58

Yes I can. Give me some time.

DanielSank

ok

I'm off to sleep, but I'm interested to see an example.

John Rennie

@DanielSank physics.stackexchange.com/questions/287442/…

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