Mathematics - 2021-05-17 (page 2 of 3)

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1:00 PM

Oh yea, then Circles. i am used to saying Balls..

my point was no

That's not what Flows meant

have you studied topology?

I am doing it right now :)

right

1:01 PM

in exception to the set itself which is open, the open subsets of R^2 must have a circular shape, right?

no

Why so?

Do you have an example of an open set on R^2 which is not a circle. (Ball)

why do you think "they should have a circular shape"

the halfplane

without 0

(x,y) forall x and all y>0

sorry $\{(x,y) : x \in \mathbb{R}, y > 0 \}$

I think open balls generate the topology though

Oh okay i see my error. But why do you exclude zero from the half plane?
Also why can x not also be bigger than 0 ?

Arent these also open sets?

that was just an example you asked for

1:05 PM

Yes i mean. if we add the zero, will your example hold?

if you include $y=0$

then no

@Flows. correct

you cant find an open neighbourhood around $(x,0)$ such that the neighborhood is a subset of $\{(x,y) : x \in \mathbb{R}, y > 0 \}$

sorry that should of been $\{(x,y) : x \in \mathbb{R}, y \geq 0 \}$

Yes i see.

if we say the first quadrant of the cartesian system without 0,0. we will also have an open ball?, therefore ${(x,y):x>0,y>0}$

Sorry open set

that set is not open

think about it liek this

then im going

when you have a set and you want to determine if it is open ( in the topology you are interested in above)

ask yourself if you can consider any point in that set and draw an open ball around that point, SUCH THAT the open ball is a subset of your set

note the radius of that ball can be as small as you want ( but of course NOT zero )

1:10 PM

Alright, got you. But then that set would be truly open ( i miswrote the bigger equal sign, should be only bigger)

${(x,y):x>0,y>0}$ this set is open ( i think you edited your post )

Yes!

see you

I see thanks. i got the concept.

no worries

1:53 PM

i now know how to prove two subspaces are identical

i am invincible

how can we find the laplace transform of $t^3cos(4t)$??

is it by using Cos= re(e^ix) ?

hello

oh wow it worked

lol

2:31 PM

@satan29 use feynman's trick

f(s) = int e^{-st} f(t) dt

something like that

differentiate both sides with 's', you get a 't' to pop out in the integral

3:07 PM

Does Cauchy requirement imply a montonic sequence? (It seems to me that this is a reasonable suggestion) If so, could you guide me on proving this?

remind me what that means

the cauchy requirement

you mean a cauchy sequence?

Yes. I have written a proof, let me type it in

if so then I dont think so

$(-1)^n \frac{1}{n}$

doesnt that fail?

Is this a cauchy sequence.

Oh yea. I just drew it. looks cauchy to me.. and its not monotonic

Guess not..

Cauchy means that points in the sequence get arbitrarily close for large indices. Why would that imply monotonicity?

3:13 PM

Yes... i understand now.

does this mean that theory where it says each bounded and montonic sequence is convergent always goes one way (thus not every convergent is monotonic and bounded)

not every convergent sequence is monotonic - you can come up with some counterexamples yourself

Is not the example you provided is such?

however, it is true that every convergent sequence is bounded, good exercise

yep

2 hours later…

5:14 PM

I think I will be one of those sad creatures that leaves MSE.

(https://math.stackexchange.com/a/296818/695930)
i am having a hard time understanding a critical part of the proof provided by Brian M. Scott. At the part where he states:
Show that for any $ m,n∈, |x^m_k-x^n_k|\le d(x^m,x^n) $ and use this to conclude that the sequence (1) is a Cauchy sequence in R.
I do recognize the truth behind the inequality, however i fail to see how proving this inequality promotes the sequence to a cauchy one, regarding the definition, should not it be for all epsilon and for all m, n bigger than a spesific N not any m n?

I get this notification "amWhy has invited you to join Trash. See your invitations."

5:26 PM

i think sometimes removed messages get put in Trash and there's a chat about it?

i got one of those too once, very confusing

mad, given epsilon, use the fact that the sequence in X is cauchy to get an N for which m, n >= N implies d(x^m, x^n) < epsilon

from what you have deduced or what he asks you to deduce, the same N will then work to show that each component sequence satisfies a similar inequality, for m, n >= N

and hence by arbitrariness of the epsilon is cauchy

Interactions with one particular user are inexplicably toxic.

Moderating is within scope, pointed pointless (:-)) comments & judgements are not.

user image

Any hints?

i'm tempted to begin tearing into your answers in the comments just to see what will happen.

:-). Frankly right now I am just sad.

@Leslie Townes. Hello Leslie, thank you for taking the time to reply to my message.

I do not understand why such sequence as he defined to be the sequence of elements out of cauchy sequences is in itself a cauchy sequence. Is this some inherit Trait?
As far as i understood this needs to be proven separatly. Thus we continue with the inequality. We choose arbitary m n and show that for these two elements we will find an element bigger or equal. So far i understand, however how does this carry that for all other following elements the distance will be smaller than this element ?

I know i am misunderstanding something, however i can not tell what....

5:36 PM

it's not an inherent trait as much as it is a property of the metric they're putting on the sequence space

The metric takes two sequences and constructs the supremum out of the substraction all their elements.
if we have elements $a_1^1, a_1^2, a_1^3 , a_1^4 ... $ where as each element is the first element of the kth cauchy sequence what does this imply to those elements ? Could you elaborate i am not sure i follow

if i have sequences a and b, and i tell you d(a,b) < epsilon, then from the definition of d, you can deduce that |a_k - b_k| < epsilon holds for all k (where subscript k denotes the kth entry of the sequence)

True. i get that.

this isn't automatic from the metric space axioms, but follows from the formula for d. it might help to prove that d is a metric if you haven't already

I have. And i understand this part well. i am not sure you understand my question.

5:44 PM

so suppose x^n is a cauchy sequence in X, and you want to show that the set of 10th coordinates of elements of the sequences x^n is cauchy in R

Can anyone help me with this? Thank you! math.stackexchange.com/questions/4140201/…

given epsilon, the goal is to find some N for which n, m >= N imply |x^n_10 - x^m_10| < epsilon

because you've assumed the sequence of elements of X is cauchy, from epsilon, you can certainly find an N for which n, m >= N imply d(x^n, x^m) < epsilon

and (by the inequality above, or the definition of d) that N happens to work for achieving the goal

But this is exactly the problem.

How do you just assume by constructing a spesific sequence and say it is cauchy without proving it is cauchy. (In his proof, he named it sequence 1)

I am trying to understand, why that sequence exist and why it is a cauchy sequence.. surely one can not just construct random sequences and say they are cauchy sequences?

you're not constructing a specific sequence

to prove that a metric space is complete, you need to prove that any cauchy sequence in the space is convergent (in that space)

so you assume, at the outset, that you have a cauchy sequence in the space

and then somehow prove (from an assumption that the sequence is cauchy) that it has a limit

so almost any proof that X is complete is going to begin with something like "let (x^n) be a cauchy sequence in X," and proceeding from that assumption to show that it's convergent

you don't have a lot of control over what (x^n) is, other than that it is assumed to be cauchy

I am not talking about $x^n$, rather sequence (1) please see how he constructed it.

5:51 PM

yes, he's fixing some coordinate k and looking at the sequence of real numbers x^n_k

Yes!

i chose k = 10 above because the analysis would be the same in any k and i try to reduce the number of symbols wherever possible

Well, K is a constant number (not index that runs over some Indexset). You surely mean the superscript.?

i was just trying to reduce the number of letters. maybe focus on understanding why the sequence (x^n_1) of first components is convergent

if you're wondering why he would think to look there, the high level explanation is that X is a space of sequences in R, and R is known to be a complete metric space. so he's hoping to use that somehow

@Rover use the triangle inequality

5:55 PM

He first shows with the given inequality that this constructed sequence of taking Elements out of Cauchy sequences is cauchy in order to use the completness of R to say that it converges

@satan29 Triangle inequality , here?

yes. this is a common theme in proving that metric spaces are complete. you start with a cauchy sequence (x^n) in the space. to show it converges to something, you generally need to first exhibit an element x of the space, and then show that d(x^n, x) goes to 0. hard to prove the second part without the first.

here he uses the existence of the componentwise limits to 'construct' the element x. its kth element is the limit as n goes to infinity of x^n_k. this makes sense because the componentwise limit was shown to exist.

But this is not my problem

is it with proving that d(x^n, x) goes to zero?

no

I am quite confident that you are misunderstanding me. Let me try to explain myself and see if we are on the same page:

I 100% understand all the proof and what and why he is doing everything.
The only issue i am having is when he constructs the sequence:
$ \langle x^n_k:n\in\Bbb N\rangle=\langle x^0_k,x^1_k,x^2_k,\dots\rangle\tag{1} $
Each element of this sequence belongs to a cauchy sequence (so first element is the kth element of the cauchy sequence 1... and the second is the the kth element in the cauchy sequence 2.. and so forth )

6:04 PM

i'm not sure what you mean by "the cauchy sequence 1," "the cauchy sequence 2", etc. the sequences x^1, x^2, ... are just elements of X. so x^1 is a bounded sequence, but it isn't necessarily cauchy (and in general will not be). same for x^2. and x^3, etc.

are you looking at the answer given by @Brian M. Scott?

yes. he forms the sequences of kth coordinates of elements of the sequences x^1, x^2, x^3, ...

the sequences x^1, x^2, x^3 are not necessarily cauchy sequences. but they are bounded sequences

but he says at the start of his proof that these $x^n $ are cauchy sequences.

he says that the sequence (x^n) is a cauchy sequence. this means, it is cauchy in X.

because X is a space of sequences in a metric space, it makes sense to ask whether individual elements of X, such as x^1, or x^10, or whatever, are themselves cauchy sequences in R. but that's not what he's assuming.

@Rover yes. Let a= |z| and b= -4/|z|

6:09 PM

and it won't generally be true that those sequences are cauchy in R. if you're worried that there's no provable relationship between the limit of x^1_k as k goes to infinity, and the limit of x^10_k as k goes to infinity, you're right. those limits could be entirely unrelated to one another or fail to exist

Yea so $ x^n $ are cauchy, then we have this new sequence, lets call "L" , L consists out of the KTH element of those Cauchies, right? Written as a tupel

then use | |a|-|b| | < |a+b| < |a| + |b|

mad, it might help to say where something is cauchy. the sequence of elements (x^1, x^2, x^3, ...) is cauchy in X.

But these are not elements, these are Sequences themselves.

the sequence x^1 need not be cauchy in R. the sequence x^2 need not be cauchy in R. you don't have to prove that (which is good, because you wouldn't be able to, under the given hypotheses)

6:11 PM

Yes That is true

x^1 is an element of the metric space X

Yes, but it is a sequence, right?

yes. it is a sequence of real numbers.

the sequence that is assumed cauchy at the outset of the proof is not a sequence of real numbers, but a sequence of elements of X

I dont think thats true. Are you referring to the sequence ( L ) as i called it or (1) ?

i am referring to the sequence (x^n) for which he says "Let (x^n) be a Cauchy sequence in X"

6:14 PM

Right, usually this set is referred to L infty and is the set of all bounded reel sequences, so x^n would have reel elements

The author failed to mention this.

Nevertheless, Could we take a gander at L. L Is a sequence written as tupel, this tuple has at the NTH place the KTH element of the NTH Cauchy defined sequence. Are you approving of this statement.

"the NTh cauchy defined sequence" doesn't make sense to me. the tuple defined in (1) has at its nth place the kth element of the sequence x^n

Wait maybe i am understanding the construction of this sequence falsly.

I thought that he is assuming there is $ x^n n \in \mathbb{N}$ thus we have many cauchy sequences denoted by n
And ten he takes from the first one the kth element and places it in the first place, from the second one the kth element and places it in the second place of the sequence L .. and so forth

or not ?

the elements of the sequence (x^n) in X are bounded sequences of real numbers. they are not necessarily cauchy sequences of real numbers, even if (x^n) is assumed to be cauchy in (X,d)

@satan29 oh ok, right !

Oh x^n is a sequence of sequences!

Not a sequence of reells..

6:20 PM

yeah. it may help to think of a rectangular array. x^1 is a row of numbers x^1_0, x^1_1, x^1_2, ..., then below that x^2 a row of numbers, and so on.

if you pick a row and move from left to right, all you are guaranteed to see is a bounded sequence

if you pick a column (i.e. fix k) and move down, the assumption that (x^n) is cauchy in X implies that you'll see a cauchy sequence of numbers

Okay it all makes sense now.

Sorry for going on your nerves, but this was confusing as hell lol

now let's put a metric on a set of sequences of elements of X

:)

@Rover Here is one way: Let $z=r e^{it}$. Then simplify $|z-{4 \over z}|^2 = 2^2$ (it will involve $\cos 2t$). multiply across by $r^2$ and solve the quadratic in $r^2$. figure out what value(s) of $t$ will give the largest $r^2$. then compare the results (takes some working with surds).

I gotta catch my bus now, but much thanks for coping with my idiocity

he said "surds." he's a spy!

@mad, no problem. enjoy your bus ride

6:24 PM

is surd not used in the usa?

most a-surd-edly not

you would think after almost 4 decades my vocab would have been pruned

You avoided prunes and had raisins instead.

:-)

i need to work on my emotional intelligence. i came perilously close to deleting my account.

Oh, you would miss us.

6:26 PM

another one is "BODMAS" instead of "PEDMAS." when in reality nobody should saying either one of those

i would.

which is sad (no reflection on you)

@Leslie I never was taught that garbage.

Hrumph. It reflected regardless.

PEDMAS means never having to say 'i understand'

my kids spent more time on ordering of operations in elementary school than i have in my whole life.

It's clearly KlaPoPuS

6:27 PM

:-)

Klapopus is the horned goat man who steals children and leaves presents around christmastime

It seems ArcticChar is going through and editing age-old posts. I find this so annoying.

omg.

Questions I answered three years ago are now appearing as active.

i will spare you my diatribe on cured operations.

6:31 PM

@copper.hat ok .

one cured operator keeps asking me why i answer "low quality questions" if not for the rep.

don't they understand we are all hanging onto sanity by a decreasing number of very thin threads, one of which might be this hellsite

@Rover there may be a smart way to do it, but grinding through will work fine.

I would dispute that. Neither of you is sane.

@Rover Someone mentioned triangle inequality (although gave the wrong version of it to you). Have you thought about that?

i am reminded in this chat room that there are decent folks on the internet :-)

6:34 PM

Where?

not seeing any

:-)

i was thinking of a triangle inequality based argument too, but i would have done it the way copper suggested

Way too much work for me.

my general approach ordering is draw a picture, compute, think

6:36 PM

We only care about $|z|$, or am I misremembering the question?

@Rover i am getting the answer as $1+\sqrt{5}$

that's right, just maximizing |z|

@TedShifrin why is it the wrong version?

Correct @TedShifrin

@satan29 that is the correct answer

You want $|x|-|y|\le |x-y|$. You had stuff with absolute value of the sum.

6:38 PM

well yes, the other part was redundant in this particular problem, but I thought Ill give the full description of the triangle inequality...

i do like the visual of that inequality. distance between two points on two concentric circles is at least the difference in radii.

maybe i'm a geometer after all.

@satan What you wrote is not useful. What I wrote is used all over analylsis.

@leslietownes It's looking more that way, yes.

It's usually called the reverse triangle inequality.

oh hmm

Oops. Too late to repair the typo. Analysis.

six cups of tea today and it isn't even lunch.

6:50 PM

i hit that a few mins after waking up

very civilised

i am now microwaving the dregs

not so civilised

Ted's suggestion is very neat and quick, but I don't see the geometry aspect.

i switch to herbal tea in the afternoon so i'm not bouncing off of the walls. i just put the kettle on because if i brew it before noon it doesn't count.

unless you mean $2 \ge |z| -{4 \over |z|}$ but that is analysis to me

Oh, Leslie was interpreting the reverse triangle inequality geometrically. I'm appalled.

The smallest distance between $x$ and $y$ is the difference $|x|-|y|$. He interpreted that in terms of circles (working in $\Bbb C$ or $\Bbb R^2$).

the geometry even lets you see the case of equality and when it's as far from an equality as possible for fixed |x| and |y|. that's good clean fun.

I see. Somehow beautiful geometric solutions only occur to me after I have climbed the analytic side of the mountain first.

6:56 PM

shakes head at what's become of leslie

i think one thing that separated good analysis from great analysis in my education was the extent to which attention was paid to the case of equality in proved inequalities. even if it was only to say 'this is complicated but there's a paper on it somewhere' or 'nobody knows the optimal constant C that works here but some goofballs have proved bounds on it'. real life is never as simple as AM-GM but it is nice to know that people care about that stuff.

Yes, in a lot of hard analysis, one has no idea what the constant(s) is (are).

people's guesses often involve geometry. "we think this has something to do with curvature" is something i heard a lot.

For example, the largest (embedded) tubular neighborhood you can take around a submanifold depends on two things: the closest far-away points can get to where you are, and the curvature of the submanifold.

my last paper tried to identify some constants. we couldn't. the editor wanted to throw out a section where we included some numerical bounds we were able to prove, i think mainly because he hated numbers with decimal points in them. even though they improved on what was known. we fought for them and they stayed in.

7:06 PM

Is this an example of a pyrrhic victory?

yes. although the paper was cited last year by some goofball, my only 2021 cite.

history will acknowledge my greatness. i'm like vincent van gogh.

I never ever looked up citations of my work, except once before a promotion.

Of course, those were the journals-in-the-library days, long before internet and searches.

i got an email ping somehow, maybe from researchgate.

7:41 PM

I am taking my computer in for service today and they can't promise it back for 3-5 days, though last time I had it in for this same exact problem it only took a day. I will be able to check in on mobile, but I hate mobile browsers.

only one computer?

browsing on my old raspberry pi is not particularly fun

I have only one computer, but with robjohn's line of work, I'm a bit surprised he has only one ;P

I don't think I've ever repaired my Macs. They go 6 or 7 years and then I just replace them.

I usually replace my laptop every year or so. Its a deduction so at least some savings. The cost of it dying is about 2wks work.

Just had a reminder this morning that a replacement is overdue. I hate tthe waste though.

whenever i get a new one, i keep the most recent old one so i have a backup in case things go haywire.

i also have a crummy old laptop that i mostly use as an input to the TV. in a pinch, i could be on here with it, bothering people.

i run a vmware instance so i can move my stuff quickly when needed. i don't need high performance on my laptop so this is a workable solution.

8:04 PM

@copper.hat Join the club :)

You can also read jack's therapy session

62

Q: How to deal with "discomforting" downvotes?

I have noticed that recently the downvoting spree on MSE has increased by a lot. It often occurs (also here and here) to me that, driven by my will to help people, I provide a solid proof/hint and suddenly It gets downvoted because it is "too advanced"; It gets downvoted because the OP did not ...

discussion down-votes

8:23 PM

That was 5 years ago.

do you think the advice is outdated?

@Onir It is really one user who seems to have a slightly punitive attitude towards me (quote "We need downvotes to delete this question.") and their comments are borderline abusive (in my opinion), certainly not the standard I expect from MSE.

One user or one mod?

Yeah I'm pretty sure I know what you're saying

this is my new dope account

dope or dupe?

8:28 PM

@TedShifrin A user, not a moderator.

dopes can be dupe

although I think that is a contentious debate

Hmm, if an ordinary user is being abusive, that user should be reported to the authorities.

I meant dupes can be dope

I apologize

It is a CURED thing.

See, @Onir. You don't even know what you're saying.

8:29 PM

who does?

Their comments (and my responses) get deleted in many cases.

always a classic

there was a support group

I never attended it though

it was called GENTLE

@TedShifrin I have always found the moderators rational & reasonable.

Because we pay them those exorbitant salaries!

I am making tons of $$$ from my MSE rep.

8:36 PM

i like acronyms.

I wish there was some sort of hedgefund i could put my rep in

my middle school had a form of detention that they'd put you in in the middle of the day, if they couldn't wait to the end of the day to get you out of the classroom. it was called SWAP. Students With Attitude Problems. i don't think that would fly these days at a public school. (and it shouldn't)

i had to stand in the corner (not quite with a dunce cap) for a while in elementary school.

had we been contemporaries at my middle school i think we would have met in SWAP.

that still happens in Mexico

8:38 PM

definitely

they would make you run around the school

and your friends would wave at you when you passed next to the classroom

or they'd just sit you in a bench outside for a couple hours

and then they'd just stare you down until you said that you were sorry

I never realized before what a good kid I was.

we used to get slapped with sticks (hands mostly)

and they'd give you another chance

that was the funniest thing about my high school. we had a lot of students who were recent immigrants from mexico, and once they realized that the teachers wouldn't/couldn't do most of the things they had been punished with in mexico, it was gloves off.

i picked up a lot of good misbehavior tactics.

8:40 PM

it became a sort of competition to see who could get the most slaps.

now, on a freezing morning, despite your hands being numb, a slap hurt like hell.

we didn't get slapped

but we did have this game where you slap the other persons hand if they don't have fast reflexes

do you know that one?

yes.

one person puts his hands in his pocket and the other person puts his hands together in front of him

in secondary school we often got kicked and hit by straps. sounds much worse than it really was.

and the person with the hands in the pocket slaps the others hands until he misses

and then its the other ones turn

8:43 PM

nothing compared to a downvote from User *****, however :-)

maybe I should start downvoting copper to see what all the fuss is about

the only time I sort of got mad was when I went in the "recently deleted" section and I found out a bunch of my answers got deleted without me knowing

:-). it really is the comments that are added that incense me. i have a few questions with a downvote or two. but yesterday i got 4 downvotes on one answer (a correct one), presumably for punitive purposes.

So is this particular user known for any good answers, or just for being obnoxious?

I'm sure there's good answers in the mix

8:46 PM

@TedShifrin I don't know, I haven't really looked. I do know the user was suspended many years ago for suspected plagiarism.

known for a wide assortment of things, some good :)

Ah, upstanding stellar citizen.

A fairly high rep user.

If it's somebody with a user***** name, I'll never pay much attention.

I am sure you would recognise this one.

Thank you for letting me vent :-)

8:49 PM

yeah no problem

I don't want to let someone else's behaviour dictate my own.

Well, for example, I've never known of Onir in all my years here.

suspected plagiarism is also kind of funny. there are all kinds of math.SE police. the PSQ patrol, the exam taker shame bridgades, the wardens of contest problems with numbers like 2021 in them

I really wish there wasn't so much drama

i do not answer these questions, i merely preserve them for future generations of contest takers

this was my solemn vow

all of that is to some extent good and necessary but when it's turned up to 11 i want to curl into a ball and cry

8:51 PM

well, storage space is sooo expensive these days i can see why there is such a rush to delete & cleanup.

one should first ask his contest problem with a slightly smaller number with "similar" divisibility properties

and then suspect 2021 is actually special

:-)

yeah I agree

yeah these kids don't understand it. change 2021 to another number. say it's from the 1978 university of chisinau entrance examination

too bad deleting a question actually adds storage space needed

8:53 PM

is there another t-shirt if you reach 200k rep? some incentive for me perhaps?

i do like the stack exchange mug, but would prefer if it as an MSE one

I still think I'll resign when I get to 100K.

I already have so much merch from when I went to programming contests and stuff

I don'r even like the stuff anymore

they should give you a fez when you hit 100k

I have like 15 trash quality backpacks

i have lots of vendor wear and the like from over the years (including a little beach ball from my first company)

i would def go for a tommy cooper MSE fez

8:56 PM

I also got a shirt from a bank that keeps calling to shove a credit card down my throat

i have a frisbee from silicon graphics, for some reason

I turned it into a rag

after they called me one morning

i have a eda tools vendor mug that says "size matters" (i inspired that one :-))

what's eda?

We always knew you were risqué, copper.

8:58 PM

it isn't a full day on here without a guided tour of the gutter

Automatización de diseño electrónico

La automatización de diseño electrónico (del inglés Electronic Design Automation, o simplemente EDA) se refiere a una categoría de herramientas de software enfocadas en el proyecto, concepción, y producción de sistemas electrónicos, abarcando desde el proyecto de circuitos integrados hasta el desarrollo de placas de circuito impreso.[1][2] Esta categoría de aplicaciones también es referenciada con la sigla ECAD (del inglés Electronic computer-aided design).[1] == Historia == === Inicios === Antes de EDA, los circuitos integrados se diseñaban a mano, y se desarrollaban manualmente. A...

that is (was) my life.

machines that build machines. trying to put skynet online.

One of my best friends started out doing some CAD designs at fiat chrysler

but he didn't get the position and now he does e-commerce

here is the mug (plus a gratuitous one of my company): imgur.com/WtqMhYm

9:05 PM

went with a very 1990s font for 'size matters'

that would be the correct timeframe :-)

Jasper started life as Tempus Fugit, Inc.

at least it wasn't Magnitudo Pertinet, Inc.

will keep that for next time :-)

scary amount of $$$ and resource goes into place & route for chips.

one vexatious thing about that whole industry is that design is often done here but manufacturing is almost never done here, and companies tend to concentrate their IP in one or the other but not both. so you often have to deal with foreign law firms and parallel proceedings instead of just one good clean american lawsuit.

they should fix that, for my convenience.

Well, you're the lawyer. File the appropriate legal paperwork.

9:14 PM

:-) the consequences of offshoring were known well in advance, but there was no incentive for an individual player not to offshore.

sometimes i can't! it's the worst to have meetings with a client that end with, "so, uh, you'll need lawyers in china for this."

"we're happy to bill you for strategy, but we can't actually do anything for you"

whatever do lawyers do in china? i'm thinking macdonalds in beijing in 1994.

good question. i don't know the system at all. a lot of it is more driven by judges than the parties, and a surprising amount of it is behind closed doors.

i have a few friends there. not a terribly transparent process.

A world full of Rudy Giulianis ... material for nightmares.

9:49 PM

back on my wife's computer.

is the triangle inequality applicable to any vector in R^n?

to any pair of vectors in R^n, yes, if the | | is given the usual meaning. and even sometimes when | | is given non-usual meanings.

it applies in any normed space.

@robjohn What is ailing your computer?

the usual abstract definition of 'norm' takes the triangle inequality as an axiom but you can prove it for many things that people informally refer to as norms without having the abstract theory in mind.

9:56 PM

@TedShifrin Li-ion battery swelling

Just don't go overboard and lecture on which norms come from inner products.

that is very polarising

Ah, I had to junk my old iPhone 6 for that, @robjohn.

I can see copper's good mood has returned.

I had the computer 4 years, then had to have the battery replaced in 2019. Less than two years later, it is doing it again.

Time for a new laptop.

9:58 PM

@TedShifrin I had the battery in my 6+ replaced earlier this year because it was not holding a good charge.

my experience with hardware is that 2 years is a business risk, 4 years is a domestic risk :-)

I got a replacement phone for $49, but took the plunge for my birthday and bought a 12.

@TedShifrin I have one, but I need to do some finagling to get the OS transferred. When my laptop comes back, I will finagle.

Ah, yes, such things are such fun.

@TedShifrin Yeah, I am going to get a 12 for my wife and me

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