The h Bar

Well, it's because the $\sup$ is the upper bound of the set, and 0.9 repeating is the largest number in the set, which is basically equivalent to 1 (and I know you said not to say that, but I don't know how else to word it).

0celo7

2:15 AM

Ok, .999999... is nonsense. What does that number even mean?

Alright, looks like we need a theorem.

Let $A\subset\Bbb R$. Let $s$ be an upper bound for $A$. Then $s=\sup A$ if and only if $s-\epsilon$ fails to be an upper bound for any $\epsilon>0$.

In other words: the sup is an upper bound such that any smaller number is no longer an upper bound.

heather

wait, isn't $\epsilon$ normally used in limits? (sidebar, I know, but it looked familiar)

0celo7

$\epsilon$ is used universally in mathematics for a "small" number.

heather

ah, okay.

hmm, I guess that makes sense.

but then how does this apply to $(0, 1)$?

0celo7

So even if we make $s-\epsilon$ really close to $s$, it fails to be an upper bound.

Do you want to prove that?

Or apply it first?

heather

probably apply it first.

0celo7

2:20 AM

Right, so take $s=1$.

heather

okay, got to go, see you tomorrow.

0celo7

wtf

Ok bye

heather

sorry for the suddenness, my dad is ready

0celo7

ready?

user218912

hiiiiiii

0celo7

2:25 AM

I'm gonna do some analysis exercises

user218912

k

user218912

i'm gonna do some qft exercises.

0celo7

@obe wtf

oh my god you're obe

god dammit people change your avatars

user218912

what?

0celo7

you look exactly like @Obliv and you have the same names basically.

user218912

2:31 AM

hmmm

0celo7

@Obliv change your avatar to something not blue

user218912

nooo

user218912

hb everyone has a blue avatar.

0celo7

hb?

I have lots of blue books you know

user218912

same

0celo7

2:36 AM

is this too dark?

user218912

yes

0celo7

what about GSM books?

I have...many

user218912

springer physics books are really blue

0celo7

Lecture notes in physics?

user218912

yes.

user218912

2:39 AM

also I made blue avatars for you guys

user218912

@ACuriousMind

0celo7

...

user218912

0celo7

oh my god

user218912

@0celo7

user218912

2:40 AM

user218912

@SirCumference ???

user218912

0celo7

...

user218912

:D

0celo7

@obe Do this exercise and I'll change my avatar.

user218912

2:41 AM

I don't know analysis...

0celo7

$\limsup a_n=\liminf a_n$ iff $(a_n)$ converges.

user218912

:(

0celo7

requires basic calculus and algebra

user218912

I know.

user218912

we were doing stuff like this in analysis

0celo7

2:44 AM

Ok, one direction is trivial.

And in the other direction you want $\liminf a_n\le \lim a_n\le \limsup a_n$.

Then apply Trichotomy

@DanielSank Evening.

user228700

2:59 AM

Hello :-)

DanielSank

3:11 AM

@0celo7 hi.

@Kaumudi hi.

0celo7

How would one go about proving the Borel sets of $\Bbb R^n$ don't contain all susbsets of $\Bbb R^n$?

user116211

4:10 AM

@0celo7 Wouldn't you need Axiom of Choice for it?

0celo7

Need?

I reject AoC, as should you.

user116211

I think Royden has the derivation with Axiom of choice but for $\mathbb R\,.$

user116211

@0celo7 :(

user116211

He uses the Axiom generously over most part of the book.

0celo7

That's fairly nontrivial

wonder how one would prove such a thing

without using that god-awful "axiom."

More like, "literally Satan."

idk how to even morally defend it

it's just pure evil tbh

user116211

4:21 AM

Why do you have so much abhorrence for the AoC? It's used by, literally, all the books I'm using.

user116211

You can't avoid it.

user228700

4:54 AM

user228700

Huh?

John Rennie

What URL are you trying to open?

user228700

Oh, never mind :-) That's just something I found funny and took a screenshot of it.

user228700

Is anybody here very familiar w/ the terms reflexive relation and identity relation?

John Rennie

In what context?

user228700

5:04 AM

I have understood the difference b/w these two terms in two different ways and I'd like to know which is correct...

user228700

@JohnRennie When defining relations b/w sets.

John Rennie

Can't help, sorry.

user228700

Oh, NP :-) I will ask someone at MSE chat maybe.

user228700

Hey, how do I type a "belongs to" a set A in Latex?

John Rennie

1572

Q: MathJax basic tutorial and quick reference

To see how any formula was written in any question or answer, including this one, right-click on the expression it and choose "Show Math As > TeX Commands". (When you do this, the '$' will not display. Make sure you add these. See the next point.) For inline formulas, enclose the formula in $......

2

\cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing gives $\cup\, \cap\, \setminus\, \subset\, \subseteq \,\subsetneq \,\supset\, \in\, \notin\, \emptyset\, \varnothing$

user116211

5:15 AM

What is your question @Kaumudi?

user228700

@JohnRennie Oh, wow, thanks! :-)

user228700

@MAFIA36790 I've asked at the MSE chat...

Shing

would anyone be kind enough to see if my answer is understandable in terms of the language? I am having hard time figuring it out if my english was not too lousy there.

0

A: Energy stored in magnetic or electric field

Energy stored in fields = the total energy required to assemble the fields It takes energy bring the charges to specific positions to assemble the field, and when you let everything go, the charges will just fly apart (the energy you "stored" in field becoms K.E. of the charges once you let them...

user228700

6:16 AM

@Shing If you're only worried about ur English then it's safe to say that u did a fine job :-) The explanation could've been done better, I suppose...

user228700

Does anybody have any thoughts on whether or not the square root is a function?

user228700

I'm having a discussion st the MSE chat but it seems like it's not headed anywhere..

user228700

NVM!

user116211

@Shing I'm not seeing any problem with that; it is good when you are talking about statics.

Shing

6:37 AM

Thank you for the help!

user116211

6:57 AM

yo @0celo7; you are still alive in the dead of the night.

user116211

7:54 AM

What is actually plagiarism?

user116211

In the context of Phys.SE.

user116211

@johnR has a very good and valid point.

DanielSank

Gearing up to make more mead!

user116211

DavidZ has also posted his answer.

user116211

@DanielSank o/

DanielSank

7:55 AM

@ACuriousMind you expressed a liking for mead. If you like, I can ship you a bottle when it's done.

John Rennie

Aha, you've just read my answer to Emilio's meta post?

DanielSank

@MAFIA36790 \o

user116211

@JohnRennie yes; I liked it.

Secret

22 people read my question so far, and still tumbleweed and still getting monopoles

Sanya

@Secret which question

Secret

8:04 AM

0

Q: Radial magnetisation cases and toroidal monopole?

Recently when re-reading Griffth electromagnetism, where he explained about how if the magnetic system is cylindrical, solenodial, planar or toroidally symmetric, then $$\nabla \cdot \vec{M}=0$$ always and thus the $\vec{H}$ field can be obtained via the usual Ampere's Law However, on closer i...

electromagnetism magnetic-fields

Sanya

hum ... not that I know the answer, but if I were you, I would add the section/page number from Griffiths book

Secret

ok

Sanya

just for people to read up the statement

user116211

@Secret The post is not even a day old; wait.

Secret

ok

P.S. page no. for 4th and 1999 edition added

David Z

8:44 AM

@MAFIA36790 start with the help center

user116211

yes, I read that quite a long ago.

user116211

It mentions:

user116211

> Do not copy the complete text of external sources; instead, use their words and ideas to support your own.

user116211

The post concerned was using the words, not the exact words, the words and the idea of the other site.

user116211

The basic flaw was that OP didn't mention explicitly the source; didn't cite the link.

user116211

8:47 AM

This is unacceptable.

David Z

Yeah, exactly. So it counts as plagiarism.

user116211

Hmm; very well then.

John Rennie

8:59 AM

13

Q: Is it good to call someone "Nerd"?

My friends always use "nerd" to describe an intelligent person,but when I searched I found that it's not really a good word. "A foolish or contemptible person who lacks social skills or is boringly studious." I've become so confused with this word. Is it good or bad??

meaning word-usage word-meaning

Yes! :-)

user116211

I never knew it meant some foolish stuff.

Secret

[Philosophy musings] People have been arguing about whether maths is invented or discovered. We could have equally apply such argument on science vs technology, with the argument that technology is not constructed, but discovered in the sense on how we found a certain configuration of known things are realisable and the properties associated to this configuration of known physics known as technology

-Above is inspired from weeks of reading abstract algebra which give me a stronger impression on how there are at least 3 different roles mathematical objects play:

1. Intrinsic abstract entities which are like objects to be unravelled of its properties
2. Tooolboxes
3. Building blocks for more complicated objects and tooboxes

Maths have this curious property that any given mathematical object can have all 3 of the above properties at the same time, thus all mathematical objects are in a sense, of the same intrinsic nature

Contrast this with physics, where models are toolboxes to understood phenomenon and predict them (and usually written in maths as a language), while the physical phenomenon itself is not an abstract entity and can be interacted with

user116211

9:16 AM

I am very bad at kinematics.... what ever I know seems not to work....😞 — user134470 27 mins ago

user116211

9:30 AM

0

Q: Differential Equation in Complex Plane

How to Solve a Differential Equation in Complex Plane, Particularly On Stokes-Anti Stokes Wedges. OR How to Solve Schrödinger equation in complex plane having complex PT-symmetric Potential.

quantum-mechanics quantum-field-theory

user116211

Homework?

user116211

WoW! Dilaton participates in review still.

Secret

9:47 AM

en.wikipedia.org/wiki/Pontryagin_duality This=fourier transform and convolution on groups

user116211

> Lemma: If an abelian group has subgroups of order $m$ and $n,$ then it has subgroup order equal to the least common multiple of $m$ and $n\,.$

Qmechanic

9:59 AM

@MAFIA36790 : It seems too broad.

user116211

yes.

user116211

0

Q: Making the Tardis with Dark Energy?

I've got a sci-fi based Physics question that involved Dark Energy... So I've been watching a lot of Doctor Who recently, and I'm very interested on how his "Tardis" is bigger on the inside. Here you can see the Tardis looks small on the outside. But inside, it's much bigger. So I've been th...

dark-energy

user116211

Oh man; this Dr. Who mania ;P

user116211

Tardis is one of the things I literally wanted to have in my childhood ;)

Qmechanic

10:29 AM

FYI: In a continuing effort to clean around here, the mods found some more socks behind the dryer. Please brace yourself for possible lost reputation points.

user116211

yeh; got the experience.

user116211

till now, + and - votes got nullified.

John Rennie

10:56 AM

-180 sock points. Not as bad as the several thousand I lost in the last outbreak :-)

As a side effect I now know one of the accounts involved. I had downvoted an answer by the puppet and I got +1 point back when the answer was deleted as part of the purge.

Swapnil Das

Hi people :)

user228700

Ah, this weekend is going to be terrible for me. Goddamn kids busting firecrackers outside my window. @MAFIA36790@SwapnilDas@Ramanujan: Happy Diwali! :-D

Swapnil Das

@Kaumudi Happy Diwali to you too :-)

I study upto 2 am and still sonic booms of crackers burst my ears.

user116211

@Kaumudi As I said earlier, use Bose or any other noise cancelling device.

Swapnil Das

@Kaumudi When is Diwali exactly?

@MAFIA36790 Bose?

user116211

11:11 AM

And yeh, happy Diwali to all too.

user116211

@SwapnilDas Google it.

Swapnil Das

Ohk. My first idea was SN Bose.

user116211

;P

Secret

@MAFIA36790 Actually, for completely unrelated premise, I do end up pondering about something similar: Consider at a playground, using chalk to draw a circular region. Next you place a ball at the centre of the circle. Now imagine the space within the circle started to expand radially at an accelerating pace. What will everyone outside of the circle see the ball had became?

user116211

ohh, lord, I don't know.

Secret

11:14 AM

I suspect due to the light from the ball need to travel longer and longer distance to reach us, and space is literally streched, the ball should become progressively more redshifted and shrunken to the outsiders...?

user116211

I don't know differential geometry yet.

Swapnil Das

Just deactivated my Quora account.

user116211

@SwapnilDas good.

Secret

me neither. But considering the above naive reasoning, eventually the expansion will be so quick that the circle will become an event hoizon as the ball redshifted into nonexistence from our view, and likewise everything in the outside world from the ball's frame. So some kind of "inverse black hole"

Swapnil Das

@MAFIA36790 Did you even?

user116211

11:15 AM

The question qualities are really bad.

user116211

@SwapnilDas I have an account; but I hardly contribute anything apart from upvoting some posts.

user116211

You need to filter tags a lot to get some really good feeds.

Swapnil Das

@MAFIA36790 I like some answers of Jack Fraser. I admire Victor Toth.

user116211

@SwapnilDas oh yeh; upvoted few of their posts too.

Swapnil Das

@MAFIA36790 It is remarkable how the latter has published 47 research papers, being employed as a software engineer and self studying GR.

Secret

11:19 AM

So in a sense, if dark energy acts by expanding space, and expanded space can indeed be confined to a finite volume in such fashion (analogous to the half plate illustrations of the hyperbolic plane), then a tardis (or any transcendential space) should be a feasible thing

user116211

Quora has some weird policy; I never could get their behind the curtain moderation.

user116211

But anyway, I don't want to speak about another site here.

Swapnil Das

I even donno about it. Same.

user116211

Their formatting facility is really disgusting.

Swapnil Das

Lol! I could never type math there.

user116211

11:21 AM

Anyway, switch to other topic.

Swapnil Das

I've decided to stay only on SEs and Brilliant.org, these are worth the time.

user228700

@SwapnilDas I...dunno, since I am from Kerala and don't celebrate Diwali :-)

user116211

@Kaumudi WTH ;/

Swapnil Das

@Kaumudi Kerelians don't celebrate? You are damn lucky.

user116211

Do you celebrate Halloween?

user228700

11:22 AM

Yes, Mallus, unfortunately, don't celebrate anything other than Vishu and Onam.

Swapnil Das

What is Vishu?

user228700

@SwapnilDas No, but I live in TN, so I've got all the bad luck in the whole world.

Swapnil Das

Oh.

user228700

Oh, Vishu is like...hm, which state are you from?

Swapnil Das

I live in Bhubaneswar, damn noisy.

Odisha

user228700

11:24 AM

@MAFIA36790 Lol, do u?

user228700

@SwapnilDas Hm, OK, I'm g'na have to look it up but u know...Bihu, they celebrate in Assam? Or Pongal in TN?

user116211

No. But we used to generally distribute candies among the children in our locality.

Swapnil Das

Yes.

user228700

That's Vishu for Keralites.

Swapnil Das

Oh cool!

user228700

11:25 AM

@MAFIA36790 Wtf? O.o U live in Calcutta, India, right?

Swapnil Das

That's Nuakhai for Odisha :)

user228700

Oh, nice :-)

user116211

Anyways, I love Diwali; my mother and grandma would decorate the whole house with diyas; it's really some memorable moments.

Swapnil Das

Halloween. I tried to scare my mother one day and that very day my specs were in projectile motion.

Anyways, learnt that its trajectory is parabolic :P

user228700

@MAFIA36790 That is so cool :-) We light diyas but we don't have so many so we only light one/two. And I haven't burst a single firecracker in life :-P Yeah, sad story. Not really tho, I don't promote the use of firecrackers.

heather

11:27 AM

hello

user116211

yo.

Swapnil Das

Yo.

Sanya

yO.

user228700

:-P

user116211

@Kaumudi I never had lit a firecracker. Neither did any of my family members.

Swapnil Das

11:29 AM

Ooh hat-trick.

user116211

My dad had accidentally burnt his right hand when some burnt firecracker fell on it from nowhere. But that's a different story.

John Rennie

@Secret Aha, you've just seen the question about the Tardis. If you're interested I've just posted an answer to it.

user116211

@JohnRennie Oops, I voted to close it as non-mainstream physics.

John Rennie

Well it is non-mainstream really. I've just used the question as an excuse to rant about some spacetimes I find interesting, but none of them are really like a Tardis.

user116211

I love Tardis.

John Rennie

11:32 AM

If the question is closed I won't be lying awake tonight worrying about it :-)

user116211

In fact every nerd loves Tardis.

John Rennie

@Kaumudi November 5th is when we let off fireworks in the UK. It's always a pain for me since I have to be in bed by 9 to start work at 5 the next morning. One of the houses in my road always has a fireworks party that goes on until midnight.

Secret

well, a tardis's space is a type of space which has a finitely larger volume than as seen from the outside.

Therefore, theoretically, if we can construct a bag of gold spacetime, and then halt its expansion somehow, then you can have a space that as seen from the outside look like the size of a room, but inside is actually a football pitch

John Rennie

Still, it's only once a year and fireworks are fun. In the UK the fireworks you call crackers we call bangers. And as a boy I used to love playing with them.

user116211

@JohnRennie I loved the Mr. Bean animated episode on UK fireworks.

heather

11:40 AM

does anyone here want to look at some python 3 code?

specifically, some code that uses numpy to multiply a matrix and a vector

Secret

@JohnRennie actually, in GR, when we said spacetime expands, does the volume of spacetime literally increase (as in spacetime was created between the two objects thus making them more far apart form each other), or the geometry curved in a way to give an impression of an increased distance between two points?

user228700

11:55 AM

@JohnRennie I see :-) Bangers is a funny word :-P

user228700

@MAFIA36790 Oh, yes, me too! :-D

user228700

To be absolutely clear tho, fireworks*=fire *crackers, right?

user228700

These are more like bombs, you see.

user228700

Fireworks and so much prettier to watch. Not the bloody firecrackers, no!

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