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user218912
12:00 AM
engineers make use of theoretical developments.
 
You probably read an applied book and needed a theoretical book, or vice versa
Halmos is (apparently) the first modern linear algebra book and is pretty good at times
 
linear algebra and set theory are impossible to understand
 
@0celo7 So what kind? Theoretical?
 
@0celo7 algebra is hard I agree. I hope geometry is easier when I take those classes
 
Vector space -> Linear Combination -> Linear Dependence -> Span -> Basis | Linear Transformation -> Kernel/Image -> Rank-Nullity -> Algebra of Linear Transformations ...
What is hard
 
12:02 AM
everything
 
user218912
did you ever take a linear algebra course?
 
@ACuriousMind The problem is to show that the kernel of a linear functional is a hyperplane. But I'm looking at the proof we gave of that in class, and I dunno wtf more he wants us to do.
@IceLord yes
 
user218912
and what did you get in it?
 
user218912
:o
 
A+
 
user218912
12:04 AM
then what's your issue?
 
the course was terrible
taught by a famous mathematician who doesn't give two craps about teaching
taught at a high school level
 
You want the set of all $v$ such that $f(v) = 0$, just expand $v$ in a basis and write out what you get, you have the equation of a hyperplane
 
@bolbteppa No basis without AoC, which I reject.
 
Is it infinite dimensional or finite dimensional?
 
Not specified.
I know the proof, but I'm confused by the problem
 
12:05 AM
Are you sure, I doubt you are doing infinite dimensional
 
We did the proof in class
@bolbteppa I will write it up and post it here.
Give me 10 mins.
 
Ok, debate in an hour though
Axiom of choice is equivalent to other axioms, do you dislike all those equivalences?
 
Yes, at a watch party
@bolbteppa I dislike the whole business.
 
Say, I don't have the patience nor understanding of mathematics to read Principia Mathematica, but did it manage to prove all mathematical axioms?
 
@0celo7 And here I thought the thing with "more disjoint subsets than elements" in the absence of choice had cured you :/
 
12:09 AM
@sirC no idea what you're talking about but you don't really prove axioms
they're just things you assume to hold true
 
The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. In 1927, it appeared in a second edition with an important Introduction To the Second Edition, an Appendix A that replaced ✸9 and all-new "Appendix B" and Appendix C. PM was an attempt to describe a set of axioms and inference rules in symbolic logic from which all mathematical truths could in principle be proven. As such, this ambitious project is of great importance in the history of mathematics...
 
@SirCumference Note that "PM was an attempt to describe a set of axioms and inference rules in symbolic logic from which all mathematical truths could in principle be proven." means that all other things shall be proven from the axioms, not that the axioms themselves somehow get "proven".
 
user218912
@SirCumference that's not surprising considering all you do it go around collecting physics/astronomy facts and asking dumb questions about them which don't really improve your understanding.
 
@ACuriousMind No, I don't understand what that really means.
 
12:11 AM
god that's like something @0celo7 would read on a sunday afternoon while everyone else is relaxing.
 
@IceLord Uh, such as?
 
@Obliv no, I hate logic
@bolbteppa @ACuriousMind see above
 
The whole reason I ask questions is because I have a passion for the subject
 
I think that proves it, I don't know what more he wants from us.
 
Don't act superior just because I actively look for information
 
12:12 AM
 
user218912
@SirCumference then learn it properly by taking the right classes and reading the right books.
 
@IceLord @SirCumference why are you fighting
 
@IceLord Don't call other people's questions dumb.
 
@IceLord Buddy, do you have any examples?
Honest to god, trying to understand what you're talking about
 
@0celo7 it's things like these that when responding to them, I would get chat banned by you..
 
12:13 AM
Oh normed spaces
 
user218912
@ACuriousMind why? I call my own questions dumb too.
 
My orbital mechanics question was clearing up what I learned in my astronomy course
 
@bolbteppa The norm does not come in here
it works for any vector space
 
@IceLord Yes. I don't like that either, but if you want to insult yourself, that's nobody's business but your own.
 
@ACuriousMind can you please read the proof
 
user218912
12:14 AM
@ACuriousMind I think we are using different definitions of dumb here, my definition is not an insult. :P
 
what is dumb if not an insult o.o
I've been using it wrong all these years!
 
@0celo7 It looks correct.
 
Oh no all those people I wanted to insult but got off w/o a scratch!
@ACuriousMind you're dumb!
 
@IceLord So what's your point?
 
@HDE226868 you're especially so
 
12:17 AM
Don't know what you're trying to tell me
 
@0celo7 Dumb doesn't suddenly change its meaning because @IceLord wants to play word games :P
 
@0celo7 ?
 
And I'm rather certain you're aware of that :P
 
@HDE226868 Ignore it
 
@ACuriousMind no, I'm dumb ;P
 
12:18 AM
@0celo7 That's slightly less annoying than a friend of mine who decided to have a debate based on the idea that "everything" is the same as "nothing".
 
::sigh::
 
He was right @hde
 
So all you're doing is trying to construct a vector $v$ such that $f(v) = 0$ is always true, so if we choose some vector $v$ such that $f(v) = 0$ is true then we're done, but what happens if we choose some $a$ such that $f(a) \neq 0$? Clearly we just want to do something to $a$ to make sure choosing this random $a$ generates $v$ such that $f(v) = 0$, that is we want to choose a $v = y + \lambda a$ such that $f(v) = f(y+ \lambda a) = f(y) + \lambda f(a) = 0$, but then $\lambda = f(y)/f(a)$
 
@bolbteppa the proof is correct, so what are you doing?
 
@HDE226868 Dude, everything is nothing. You have to, like, broaden your horizon, man
2
 
12:20 AM
Well what's your problem with it, I just explained the logic of it, why do you have a problem
 
user218912
@SirCumference you'll realize it someday.
 
I understand the logic
 
Speaking of debating, three people in my statistics class are anti-Semitic and claim the Egyptians won the six day war.
 
I don't understand why he assigned the problem
 
Quel problemo
 
12:20 AM
my proof there is word-for-word the proof he gave in class
 
@ACuriousMind That sounded pretty nihilist.
 
I ask them why Egypt lost land and Israel gained land, they couldn't answer
So they told me to kindly go die
 
What is the exact statement of the problem
 
@IceLord Realize what? I'm taking the courses I'm asking about -.-
 
user218912
no you're not.
 
12:21 AM
I'm sorry?
What?
 
user218912
are you in GR?
 
@HDE226868 It was supposed to sound stoned, but I guess I'm not good at pretending :P
 
I'm taking astronomy
I asked about orbital mechanics
What's out of my reach here?
 
user218912
I'm referring to your other questions.
 
@acuriousmind Shaw, dude. Like, totally saw where you were coming from.
 
12:22 AM
Which?
 
@ACuriousMind Yeah, man. Far out, but, like, not.
. . . That wasn't any better.
 
@HDE226868 Holy crap
 
also can you remind me what the difference between the normalizer and centralizer of a group was? @acuriousmind I think the normalizer was $N_G(A) = \{g\in G \mid gAg^{-1} = A\}$ where the elements in the normalizer leave the set $A$ unchanged. Whereas, the centralizer is more specific $Z_G(A) = \{g \in G \mid gag^{-1} \forall a \in A\}$ is this right?
 
Mercury found to be tectonically active, joining the Earth as the only other geologically active planet in the Solar System
 
@Obliv Can't you just look at the Wiki article for the definitions?
 
12:24 AM
@SirCumference I thought Mars had evidence of tectonic activity.
 
@acuriousmind why would I do that when I have you?
 
Also, given the past year in astronomy, that's a relatively low-key find.
 
@HDE226868 Nah, Mars died a long time ago. It's core was too small and it solidified
 
OK I'll search it up 8^)
 
12:26 AM
@SirCumference newsroom.ucla.edu/releases/… - five seconds via Google.
 
user218912
@Obliv you're taking ACM for granted, which is bad. @0celo7
 
user218912
I consider ACM and 0celo7 blessings.
 
> Observations made of the magnetic field of Mars by the Mars Global Surveyor spacecraft in 1999 showed patterns of magnetic striping discovered on this planet. Some scientists interpreted these as requiring plate tectonic processes, such as seafloor spreading. However, their data fail a "magnetic reversal test", which is used to see if they were formed by flipping polarities of a global magnetic field.
Plate tectonics (from the Late Latin tectonicus, from the Greek: τεκτονικός "pertaining to building") is a scientific theory describing the large-scale motion of 7 large plates and the movements of a larger number of smaller plates of the Earth's lithosphere, over the last 100's of millions of years. The theoretical model builds on the concept of continental drift developed during the first few decades of the 20th century. The geoscientific community accepted plate-tectonic theory after seafloor spreading was validated in the late 1950s and early 1960s. The lithosphere, which is the rigid outermost...
It's disputed
 
Idk about @0celo7 but yeah ACM is pretty cool
I think he's one of the few sources of infinite energy in this universe. He'll answer pretty much anything you ask him.
(probably because he's an A.I.)
 
user218912
12:29 AM
30% of the time.
 
user218912
@Obliv or he will say "idk what's unclear, it's obvious". and make you do it on your own.
 
@SirCumference But there's evidence for it, and I don't think these findings necessarily have the same faults (pun absolutely intended).
 
@HDE226868 Well, guess I'll have to look into it more
 
@SirCumference As will I.
Point is, yeah, that Mercury news is cool.
 
It's been 3 years since I've taken Earth Science. Does volcanic activity imply tectonic activity?
 
user218912
12:32 AM
you live off facts dude.
 
@ACuriousMind Fake modesty.
@IceLord what does that even mean?
 
@0celo7 Don't ask.
 
@0celo7 what's your profile picture
 
@SirCumference I am asking
 
He's not making sense.
Okay then
 
12:33 AM
@Obliv art
 
user218912
@0celo7 it means he keeps asking about facts and not concepts. I'm worried about him because he won't ever understand anything if he does it like that.
 
Who's in your profile picture @0celo7
 
@Obliv Travis Scott
 
@IceLord Who are you talking about?
 
user218912
@SirCumference you ofc.
 
12:35 AM
FIGHT FIGHT FIGHT FIGHT
 
@IceLord I don't know what you're even talking about. I've taken an Earth Science course three years ago.
I appreciate your worry, but don't, I'm fine.
 
@ACuriousMind Make them stop.
 
KEEP CALM KEEP CALM KEEP CALM KEEP CALM
 
@ACuriousMind Have you heard: "Let $V\subset E$ be a subspace of a normed vector space $E$. Given $x\in E$, we define the distance to $V$ by $d(x,V)=\inf\{||x-y||\mid y\in V\}$. If $V$ is locally compact (in particular, if $V$ is finite-dimensional), this infimum is attained by some vector in $V$." before?
 
user218912
@SirCumference it's obvious what I'm talking about. would you rather be a database or an a.i.?
 
12:38 AM
Anyways
 
user218912
because right now you're a database.
 
Geysers spotted by the Hubble telescope on Jupiter's moon Europa may allow us to search for life beneath the surface
 
@ACuriousMind Ready to be a mod? ;)
 
an A.I. could be a database in some cases. @acuriousmind is probably on his way
 
I wonder if gen. pop. hurr durr you too hostile hurr durr will actually matter in the election
 
12:39 AM
@Danu New version of profile pic?
 
@Danu At least my nomination comment thread is the fastest growing :P
 
@HDE226868 Yeah, friggin math.se users had my old one too often.
 
@Danu The darker look suits you
 
@Danu I've had that issue, though not among the Math users.
 
Found this interesting
 
12:40 AM
@ACuriousMind More "me" ;P
 
user218912
boring.
 
oh come on
why are you so hostile towards him all of a sudden
 
@IceLord Thanks for your opinions IceLord. I've been kept up all night wondering what IceLord the stackexchange user thinks of that video, but now that you've graced us with your thoughts without anyone even asking, I can finally sleep at night. Thanks again, IceLord, this next one's on you.
Jesus christ it's 2:00am
 
@SirCumference whoa what time zone are you in???
 
12:43 AM
@0celo7 Studying abroad :P
 
user218912
@0celo7 we're all friends here, idk what you're talking about.
 
@SirCumference Hmm. It's 3:44 in Israel.
 
@0celo7 Not in israel anymore
That was a few months ago :P
I can't think anymore
I've been trying to write this paper for hours
More coffee...
 
@0celo7 choose a number 1-26
 
@SirCumference Ah, yes. Deciding to go to SE chat is always a great aid in writing papers ;)
 
12:47 AM
@ACuriousMind ;-;
 
@Obliv 69
 
okay I'll take that as $69 \mod 26$
 
@ACuriousMind Can you give a slight hint to my earlier question?
i.e. "contradiction" "contrapositive", something like that
 
@peterh I need some context for your remark. I don't know what you're referring to.
 
@IceLord The hell?
 
12:49 AM
@0celo7 nice you chose one of the easiest exercises for me to do. Find a presentation for $Z_n$ with one generator.
 
@0celo7 I think we did that in FA, but I can't give an off-hand hint about it.
 
user218912
nvm that's a dumb question.
 
I'm sick of stats. It's like math, but boring.
And so much writing
 
@ACuriousMind ok, can I bounce some thoughts off you?
 
user218912
@SirCumference astrophysics is basically data analysis. so get used to it.
 
12:50 AM
@IceLord I know. But this course is a pain in the ass.
At least astrophysics is interesting
 
@ACuriousMind A direct proof would be to take a minimizing sequence, then show that it is eventually in a precompact region.
But we have no information on precompact regions
Another idea is to go for a contradiction
we take a minimizing sequence with no convergent subsequence
But getting data on a minimizing sequence seems to be hard
 
user218912
@ACuriousMind do you know any condensed matter/stat mech?
 
I can't show that they're Cauchy
any estimate for that is uncontrollable
 
user218912
why does the isotropic motion of electrons in a metal give a vanishing contributing to electrical conductivity?
 
@0celo7 Well, but in a locally compact space, you have the infimum has a closed compact neighbourhood, no?
 
12:54 AM
@ACuriousMind whoa whoa whoa
what does that mean?
 
@IceLord I know almost no condensed matter
@0celo7 Which part is unclear?
 
"you have the infimum has a closed compact neighbourhood"
that's not even English
 
user218912
that means in 7 months from now I'll be the expert on condensed matter here.
 
user218912
unless some other guy shows up.
 
Say, how do these moderator elections work?
 
12:56 AM
@0celo7 Insert "that"
 
One vote per person?
 
@Danu still doesn't make sense
we don't know that the infimum exists
 
@sirC I think sockpuppets are allowed to vote. (KIDDING)
seriously, don't chat ban me again please.
 
@SirCumference See this meta.SE post and also note that there's a dedicated chat room for the election
 
12:57 AM
Oh, it uses the alternative vote
That's nice
May I just say this is pretty funny
 
@ACuriousMind Can you please restate that in plain language?
 
@0celo7 Mhh, I cannot
 
Finally on page 13
Got 2 pages left
 
I presume you may not use that "locally compact" and "finite-dimensional" are, in fact, equivalent? :P
 
I may use that.
@ACuriousMind I don't want you to explain more, I literally have no clue what you were trying to tell me :/
 
1:09 AM
Well, I'm not sure I tried to communicate the right idea. Now I'm more thinking that you show $V$ is closed and locally compact, so you don't need to know anything more about the minimizing sequence to get (part of) it to converge.
 
@ACuriousMind Should I write $V$ as the span of some finite set, then compute the inf explicitly?
@ACuriousMind $V$ is not compact
It's a vector subspace
those are never compact
 
Oh if $V$ is itself compact, this is trivial.
 
You need to show the minimizing sequence is Cauchy
 
Right
Because then finite-dimensional implies Banach implies convergence.
So, we write $(v_n)\subset V$ with $||x-v_n||=d(x,V)+\frac{1}{n}$
But $||v_n-v_m||$ is way hard to estimate
 
1:12 AM
That'll involve some estimates. A proof I learned that could be adapted involves the subspace being uniformly convex
Which is true for finite-dimensional subspaces
 
1:55 AM
So, who do y'all want to win the election?
 
user228700
2:08 AM
Ya know what? Never mind. Stupid question.
 
@KaumudiHarikumar There are no stupid questions
 
user228700
@SirCumference OK, say we have a velocity vector $v$. I've resolved it into two components, $vcos\theta$ along the positive y-axis and $vsin\theta$ along the negative y-axis.
 
user228700
Without prior knowledge of the fact that $vsin\theta$ is along the negative direction of the x-axis, is there no way for me to know that I must write it as a -$vsin\theta$? Idk, this may be a brainfart.
 
user228700
I've always sort of wondered about this but I shrugged it off, every time. I'm pretty sure that this does qualify as a stupid question though...
 
user218912
I have a dumb question, why is the atomic radius difference between rubidium and cesium smaller than the radius difference between sodium and potassium?
 
2:13 AM
Perhaps this might just be me unable to think at 3:13am, but why would Why would $vcos\theta$ be on the y-axis?
 
@KaumudiHarikumar This entirely depends with respect to which axis and in which direction you are measuring $\theta$
 
user228700
@SirCumference It's oriented weirdly.
 
user228700
@ACuriousMind OK..? What do u mean?
 
user218912
shouldn't it be the opposite?
 
From what you've written, it sounds as if you are measuring $\theta$ counterclockwise with $\theta=0$ being parallel to the positive y-axis.
 
user218912
2:14 AM
@SirCumference do you know?
 
@IceLord Do I know what?
 
user228700
@ACuriousMind Yep, that is the case.
 
user218912
1 min ago, by IceLord
I have a dumb question, why is the atomic radius difference between rubidium and cesium smaller than the radius difference between sodium and potassium?
 
@KaumudiHarikumar Okay, so what exactly is your question about that?
 
@IceLord Aren't rubidium and cesium in different periods?
 
user218912
2:15 AM
@SirCumference yes but same group.
 
user218912
why does that matter?
 
@IceLord Why would you expect it not to be smaller?
 
user228700
@ACuriousMind I'm a bit of an idiot, so please bear with me but I was just wondering if there is no way for the components to tell me if they're pointed in the i or -i direction. Kinda like how the direction is taken care of in cross product of two vectors, u know..? God, my question sounds increasingly dumb as I keep typing.
 
user218912
@ACuriousMind high school level answer: there is more shielding of the nucleus at higher energy levels, so I expect it to be larger.
 
user218912
@ACuriousMind can you disprove me using QM?
 
user218912
2:17 AM
because this is for condensed matter.
 
user218912
I need a technical answer.
 
@IceLord Ah, but the proportional difference that adding one elementary charge to the nucleus makes is much larger when going from Na to K than going from Rb to Cs
 
user218912
thanks @ACuriousMind
 
user218912
so obvious now.
 
Never knew @ACM was into chemistry
 
2:20 AM
@KaumudiHarikumar Well, by choosing to measure the $\theta$ that way, you've essentially defined that the vector is resolved as $(-v\sin(\theta),v\cos(\theta))$. If you measured $\theta$ clockwise, you would have $(v\sin(\theta),v\cos(\theta))$.
 
user228700
@ACuriousMind That. I don't understand how I've defined it like that by choosing to measure $\theta$ that way.
 
hmm. Have you drawn a picture?
 
user228700
@ACuriousMind Yep. Do u want me to upload it?
 
Not sure if that's necessary
I just want you to look at the picture and think about where the vector goes as $\theta$ increases
If it increases in the counterclockwise direction, you should see that the x-component of the vector gets more and more negative
 
user218912
@ACuriousMind what's the formula for that btw?
 
user218912
2:24 AM
I forgot
 
user228700
@ACuriousMind Um, yeah.
 
@IceLord For what? I just thought about it rather qualitatively: Going from 11 to 12 is a larger change than going from 37 to 38
 
user218912
@ACuriousMind yes but can't you prove that rigorously?
 
user228700
I've decided that it truly is a stupid question. Thanks for ur help :-)
 
@KaumudiHarikumar So, if you want to express the x-component with $v$ and either $\sin(\theta)$ and $\cos(\theta)$, observe that $\sin$ is the one that increases when increasing $\theta$, but it's positive. So you have to put $-v\sin(\theta)$ to get something that increases in magnitude but is negative.
 
user228700
2:28 AM
@ACuriousMind Hm, OK. Thank you :-)
 
@IceLord I don't think you can analytically compute the atomic radius.
 
user218912
alright. I thought you could.
 
user218912
thanks :)
 
user228700
I've got one more quick question! Centripetal force is described in my textbook as "...accelerates the body without changing the speed of the body". Is this always the case? Can the term " centripetal force" be used only in the case of uniform circular motion?
 
vzn
2:44 AM
@KaumudiHarikumar not sure what you mean. afaik its typically for circular motion but any curves will have an element of circular motion. ps saw you talking about your mom questioning your choices of physics as a major, wondering if she has any new pov on that...?
...
 
Howdy dmckee
 
Hi, everybody.
 
Hi @Daniel
Watched the debate? :P
 
nope
Was out to dinner with a visitor.
Was it good?
 
2:53 AM
It was pretty funny
in Mathematics, 2 mins ago, by Danu
The bit where Trump ranted about how he has "good temperament" while talking over the host of the debate was great.
 
@Danu Amazing.
 
Also, he refused to admit any mistakes regarding the Obama birther thing, repeating numerous times that he did a "good job" getting Obama to produce his birth certificate
Other thing, pretty great, was that while Hillary was talking about how he did not pay any taxes, he said "that makes me smart" (interrupting Hillary)
 
@Danu Wow.
 
I want to say that this was a trainwreck, but I'm probably biased.
 
@Danu Dude. Sounds like he did a fantastic job.
 
2:56 AM
In any case, he went classic Trump
 
Well, Trump has two modes.
He has classic Trump wherein he says things and acts in ways that are logically ridiculous, but actually kind of charismatic.
He also has a mode wherein he insults veterans.
The former kinda works.
The latter does not.
 
Hurr durr veterans in the US :P
I don't understand this collective worship
But that aside, it's obviously a bad move for a presidential candidate.
 

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