@XanderHenderson how do you pronounce that?

pah-LO-mah?

or maybe pah-LO-muh...?

I have forgotten how to IPA... :\

@XanderHenderson do you want to home brew it?

google.com/…

@quid Ha! But I meant international phonetic alphabet, not India pale ale.

By coincidence I was just drinking grapefruit juice earlier. I guess I could find some Tequila somewhere in the depth of my bar.

I'll leave now see you all!

@amWhy : India is getting aid from many countries (a major part is from US and European countries). I think the issue of supply is primarily because the plan was to vaccinate old people first and then switch to the younger ones. But due to the alarming suitation of second wave they had to start the programme for vaccination of young adults too soon.

Loved the discussion on pronunciation of Greek letters. I have no idea of Spanish so couldn't gather much.

In Hindi also some of the original pronunciation is lost. The famous example is "Krishna" (name of a major diety in Hinduism). Experts argue that the "i" should actually be replaced by "u" like Krushna and there are diffences even there. Whether the "u" should sound like "put" or like "but".

Also the "n" of Krishna has a very different sound than the "n" of "note".

@ElliotYu: I pronounce $\phi, \varphi$ as "fie" and the difference in these two letters is just the writing style.

@ParamanandSingh I think it should be pronounced as kṛṣṇa, no as krushna

I myself say kṛṣṇa rather than krishna

@Euler2: when you have to describe the sound via writing it is better to express it using known sounds in writing.

What you have mentioned is the iast symbols. One doesn't know how they sound unless one is familiar with that standard.

@Euler2: idea was to explain it to those who don't have much idea of Devanagari script and you have to convey the sound which can be approximated by sounds of syllables in their language.

yes

It also appears that you are familiar with Hindi and you can understand how difficult it is to tell the pronunciation of Sadak (hindi word for road) to anyone not familiar with Hindi.

yes that's true

Anyway it is good to know that you know hindi as well as Russian. Have seen some of your chat messages in Russian.

well well well I know many languages because

btw sadak is sometimes written (in iast) as saṛaka

mission completed: create confusion

@ParamanandSingh russia too sir

@ParamanandSingh I mean... Really it's better to use the IPA, but not enough people use it

Not enough as in (1) the number of people familiar with it is too small, so you can't expect to be always understood in a random conversation if you use it; (2) it's very useful and I wish more people understood basics of phonetics and used the IPA when they need to describe pronunciations.

@ParamanandSingh You see... I've actually seen papers that use \phi and \varphi as distinct quantities...

@ElliotYu: yeah they are different symbols which can be used to represent different quantities. You can compare the situation with the $d/dx$ and $\partial /\partial x$. Both the symbols are actually letter "d" but writing style is different.

But still using such symbols together is a bit confusing.

I think the relationship between \phi and \varphi is probably a bit closer than between d and \partial, considering a lot of people don't recognize the latter two as the same letter.

At least in handwriting it's easier to distinguish \partial and d

Yes their appearance is quite distinct. But I can imagine a person whose handwritten "d" may look like a \partial

But more people write the letter phi closer to \varphi, and sort of recognize \phi as the "print" version, like the double story lower case a.

I also prefer to write like varphi in handwriting.

And I imagine some people justify using \varphi in handwriting because it's easier to distinguish from the upper case

That's something I did not notice until you told just now.

hello everyone! I want to start learning homotopy theory (and maybe other related subjects), so I was wondering what branches I should have covered to fully understand it.

@ElliotYu In my phd thesis, the letter "D is used to mean at least six different things (different fonts and scripts, but all "D")

@XanderHenderson Could I read your PhD thesis?

Happy May Day, everyone! Oops, and for some of us, Happy May 2nd!!

@amWhy Yes, about 35 minutes away from that!

@TeresaLisbon Whew! Well, then you're doubly acknowledged! ;D

@amWhy Haha, yeah. On a thread yesterday where I left a comment regarding enforcement of quality standards, two users (who weren't part of the question) chimed in to say they disagreed. You can see my response there, I put it on CURED. I'll tell you if I get a response so we can argue it out if required with them.

@TeresaLisbon It seems these days, they only object in "numbers".

@amWhy Yes, honestly. But having read the meta threads , I know exactly how to address them, and that's if I need to. While I've not been on the site that long (I mean , ok 63 months is quite long!) I know literally every question on meta that addresses PSQ answering, answering questions in comments, proposals banning PSQs, low effort questions etc. so thankfully I can bring back those arguments and we will do well here!

@TeresaLisbon Oh, indeed. But it is the answerers that refuse to acknowledge the evidence put before them, and so they are more apt to rally in numbers, grasping at character assault, etc., precisely because, they cannot defend themselves anymore.

So that if the same user is caught twice, we reference their instances one behind the other as reminders. If we have requisite backing and don't cross the rude line ourselves (which is a subjective line but we kind of know it roughly, and requires some patience and good sentence formation and thought) then this can work brilliantly. It's even better if the flags have less time between them.

@TeresaLisbon Indeed, and that's where teamwork can help, in terms of flagging.

@amWhy Correct, great point.

:\

I acknowledge it. I think sometimes the pro-feelings get very strong.

@Xxander I hope I handled the following comment well enough:

Granted, I posted a bare link to the meta post.

Looks fine to me.

@amWhy I agree with Xxander that it's well handled.

@amWhy That particular question really seems like a question of RTFM.

@XanderHenderson Good. I did not want to antagonize, and I did not even downvote the answer.

I don't really see the mathematical content there---it is a question of how a particular software package does a particular job.

Not really well suited for Math SE. :\

@Xander RTFM Thursday Tuesday Friday Monday ? ;P (Really, I don't know RTFM)

@XanderHenderson But it's a mathematical software in the end, and even the job asked is of a mathematical nature, whether there's a result that can make finding the minimal generating set easier. It is a PSQ, that should finish it off anyway.

Read the ......... manual.

(Note : I don't know the word in ...... , I heard it's pretty bad though!)

@amWhy Read the manual. :P

@TeresaLisbon Why the ellipses? RTFM stands for Read the manual. :P

Oh, I get it!! Kind of like the version of lol: lmao, or lmfao

@XanderHenderson Aha, the F is silent.

@TeresaLisbon Yes, the F is silent. :P

@Teresa I think it means: Read the Fracking Manual

@amWhy இவளோ கிட்டக்க வந்துட்டேள் , சொல்லியே தீ ரலாமே! (You have come so close, might as well say it!)

@TeresaLisbon Hah! ;D

@XanderHenderson Isn't there a catchy phrase I'v heard, something like "Questions using software (or programming languages) should focus on the mathematical questions involved, and not on the implementation of software, calculators, CAS, programs... etc."

@amWhy FLAGGED!

@amWhy Yeah, I should probably add that to my list of generic responses.

Ugh... I am really tired of comments asserting that the only legitimate reason to downvote an answer is if it is wrong.

No!

@XanderHenderson Fracking: the process of injecting liquid at high pressure into subterranean rocks, boreholes, etc. so as to force open existing fissures and extract oil or gas. (But as I read "the process of injecting liquid at high pressure...", hmmm).

Anyone may downvote for any reason, as long as it is tied to the post, and not the person.

The downvote arrow indicates that a downvoter is signaling that a post is "not useful". An answer to a low-quality question is, in my opinion, not useful. Thus it earns a downvote.

@XanderHenderson Indeed, and when hovering over a down-triangle, one sees: This post is not useful or....

Imma ninja!

@XanderHenderson Echo.

Typing your replies before you can!

smoke bomb

vanishes

bye

Xxander

Hendo

@XanderHenderson ;P (me thinks more gaslighting!)

Teresa Have you ever played the echo game (credit @quid)?

Nope

@TeresaLisbon Okay, just now starting, I say "echo". Now you respond with the next response.

echo echo

echo

No , hang on

is that a response?

iWin!

@XanderHenderson bzzzzzzzz! you fail.

Aw...

:'(

GOT IT!

OK yes I did.

So someone says echo, and then the next person to type echo or whatever wins.

@TeresaLisbon Correct!. Next, I say "echo, echo". Your turn.

ok

echo,echo

Ecco (the dolphin)

@TeresaLisbon bzzzzzz. Your response should have been echo, echo, echo.

echo,echo,echo

AH , OK

I fail.

Now I say, echo, echo, echo, echo, echo!

echo,echo,echo,echo,echo,echo

Notice the pattern: 1, 1, 2, 3, ...

5,6

That's : Number of rooted trees with n vertices in which vertices at the same level have the same degree

We are geniuses indeed.

The first two numbers sum to 2, 1 and 2 sum to 3. what do 2 and 3 sum to?

Ooh, I broke Fibonacci with my last response!

@TeresaLisbon Bingo! You are good!!!

But still, we've got number of partitions of n into at most four parts!

I love OEIS.

@XanderHenderson Now you can play with the big kids, (after we put you in "time out")!

@TeresaLisbon One less "echo". Then, after the correct echo, echo, echo, echo, echo,

We'd have echo,echo,echo,echo if I'm reducing by one?

I respond, echo, echo, echo, echo, echo, echo, echo, echo

@amWhy No, I'm trying to handle flags.

echo,echo,echo,echo,echo,echo,echo

@amWhy I am planning to show my kiddos Binet's formula for the Fibonacci sequence next week.

@XanderHenderson So you're already playing with the big kids, enjoy!

@XanderHenderson The proof for this that goes via matrices is fascinating, and probably the one you are doing, right? (Not induction, I hope). Or will you use Vieta's formula with the quadratic that has the two radicals as roots?

@TeresaLisbon You listed six, one less for five. 3+5 is 8, which is what I listed. Now we need 5+8 echos....

The only little conceptual hurdle I am having difficulty overcoming is explaining why a linear combination of solutions to a linear difference equation should also be a solution.

:\

@XanderHenderson Cool!

@TeresaLisbon I think that I have a more diffEQ approach to things: we make the ansatz that we should get some kind of power function as a solution (I mean, the Fibonacci sequence is almost geometric, right?), then see where that takes us.

@XanderHenderson What are you going to call your kiddos when you have in class a vet age 30, and a displaced homemaker, age 38?

@XanderHenderson That is magnificent. I never thought about that!

@amWhy Years ago, I had a 70 year old retiree in one of my classes. Despite the fact that I was less than half his age, I still called him one of my kiddos.

He thought it was pretty funny.

@TeresaLisbon It is essentially the same approach that one might use to solve a linear differential equation: assume that the solution is exponential, then figure out the details.

@XanderHenderson Hahaha, that's sweet!.

The nice bit is that the characteristic polynomial comes out in the same way, and is interpreted in about the same way, too.

So there is a nice connection which can be drawn between linear difference equations and linear differential equations.

The problem is that you really need a little bit of linear algebra to really make sense of what is meant by "linear", and to justify the statement that linear combinations of solutions are also solutions.

@XanderHenderson But it's still very sweet. What's the thought behind there being such a relation? That could do with the "finite differences" idea : the finite differences idea is basically that you take the "finite differences" of the sequence and see if there's any pattern among them. For the Fibonacci sequence, the difference sequence is self-similar, implying in analogy with the derivative in calculus, that :

the function must have exponentials/powers involved.

Maybe I will just demonstrate that if $u$ and $v$ are both solutions to the recurrence relation $a(n+1) = a(n) + a(n-1)$, then $\alpha u+\beta v$ is also a solution, and then solve for the appropriate coefficients at the end...

Yep, that's also an important idea by itself.

@TeresaLisbon Yeah, there are some strong links between differential and difference equations. Difference equations could, I suppose, be thought of as a kind of discrete time differential equation.

That isn't quite right, but it is kind of in the direction of the right idea.

@XanderHenderson Very true, the links go deeper.

(I mean, I know further links, that is!)

And numerical schemata, such as Euler's method, essentially approximate (systems of) differential equations using difference equations.

Correct, great point @XanderHenderson. Oh no, have to watch the match tonight, see you guys and good luck Xander for your next class. You may request resources from me if you wish anytime!

e.g. $fx_{n+1} \approx x_{n} + f'(x_n) \Delta x$.

Mind you, my preceding comment did not harass this user, and this was my first link for this user, to the meta post. He has been hostile, no matter how tame the suggestion.

Also, note, @Xander, I commented below four out of six answers on that post.

Sorry for interrupting, all.

@Xander, Danke!

@XanderHenderson Why can't you just show that the difference operator acts linearly?

It is a precalculus class. They have no idea what an "operator" is. The goal is to give them a somewhat rigorous derivation of the formula wihtout introducing too much theory or abstraction

@XanderHenderson Ah. Well just say that Δ can swap with addition and scalar multiplication. That is, given two sequences f,g: (1) adding them first before taking Δ is the same as taking Δ first before adding; (2) scaling all terms by c before taking Δ is the same as taking Δ before scaling by c. Since a linear combination is just a sum of scaled sequences, you can just swap swap swap.

Got to go though. See you!

I am now issuing a quidalert for @quid. Sirens and lights! (Just to find him, no emergency he has to handle!)

@amWhy I saw your name popping up in the general math chat room. I didn't read what it was about, just letting you know.

@vitamind thanks.

@amWhy 🚨🚨🚨🚨🚨🚨

@quid Hahahaha! Sorry you got pulled into the mathematics chatroom. I learned above that I "was being talked about" in that chat, and indeed, it was copper.hat claiming a threatened them. But I had not. I should have probably let them just trash me, like usually happens.

@amWhy Well, now there is ;D.

@vitamind Thanks, for letting me know. But @quid seems to want me to ignore it when a user is trashing me. Go figure! :(

@amWhy that's not what I said.

@quid By eliminating all options for me, @quid, yeah, you pretty much did say exactly that. Not everything fits the puzzle in which you choose to see the world.

Oops, I cannot post a link to another post, I guess. Sorry to offend, @quid. I sense you are not on board with the new policy. No suprise here.

@amWhy I'm not sure what your point is.

5:00 pm my time: Hence, no more mod quibbling, correcting, posturing, etc. Anyone'd like a drink?

@amWhy maybe some tea? With sandwiches?

@amWhy 3pm my time, but I am already drinking. It's Saturday.

^^quid There you go. Doctor's orders! What kind of sandwiches?

@amWhy thanks. Maybe HAM as a tribute to our new friend.

^^^ I think there's ham in those! Looks like "club" sandwiches! Enjoy, @quid, and I'll invite our new friend, too.

@amWhy looks very tasty.

@MikeWaters

@amWhy I see!

@Xander You outa beer? What can I serve you!

@quid "Ham" is not an acronym.

@amWhy Not out. But I am having wine today.

And gonna make Spanish-style tortilla for dinner.

@XanderHenderson Enjoy!!

(I can't buy potatoes in less than 20 lbs increments, so I need to figure out how to use them up.)

@XanderHenderson Yummy! I've gotten my drone up and running again, after the winter in Wisconsin. I'll test it out, sending it to you, if you'd be so kind as to load er'up with dinner, and send back to me. But I don't want to eat too too late. ;D

@amWhy I need to wake up early enough to get a sunrise timelapse. :\

But the sun is currently rising around 5:30am, so I need to actually get things going around 4:45. :\

@MikeWaters Wow. I was sure it was Home and AMateur.

@XanderHenderson Good, then I'll get dinner early enough!

@amWhy Sunset isn't until after 7.

Amusingly it derives actually from ham, well more or less at least.

Shabbos is getting later and later.

From ham as in ham-fisted if the sources I found are to be trusted.

@quid Nope. The original meaning of ham radio has been lost to history. HAM actually irritates some hams.

@XanderHenderson I'll wait!

random thought question: do you think it's possible to construct a set which contains every number?

and by every number I mean every number

@vitamind Wouldn't that be $$\mathbb C$$?

Err, the set of complex numbers?

@amWhy That was my first thought too. But unfortunately this set does not contain quaternions, octonions etc. (Cayley Dickson) nor infinitely many cardinal numbers

@amWhy The $p$-adics don't live there. :P

@vitamind Define "number".

@XanderHenderson Yup I'm already thinking of it...

(After putting the question into google it gave me "Universal set" but it must contain itself so this is not what I'm looking for)

Nor the extend real numbers. But it's a stretch to call many of the "counterexamples" "numbers", in that they cease to become comparable.

@reuns No, I'm sorry, but numerology would then become a category/tag for deletion. That's my thoughts.

@reuns No. Such questions ought to be closed / deleted, not promoted. :\

@amWhy Yes. I could always define a "new" number. That's a big problem.

@XanderHenderson Reading my mind again? Get outa my head!! ;P

I don't see what you mean, those questions are never closed, deleted, and they are often promoted.

I like the name but I mean creating a tag for those kind of questions without much mathematical content other than "please run a script to find a counter-example, or tell me that you know some genial theorem proving I'm wrong" (or right)

@reuns Can you give examples?

@reuns But those are not math questions, and math.se is not about using computing algorithms to prove something wrong. As Xander said, giving a tag to such questions would act to legitimize those sorts of questions.

Because there are a lot of questions related to the Collatz conjecture and the Riemann hypothesis which could appropriate be labeled numerology which get closed and deleted.

@reuns That doesn't strike me as numerology.

This is exactly numerology: I have a weird formula that doesn't mean anything but I like it and I run a script for a few minutes then I go on a math website to tell "look how my formula is nice". That said sometimes the answers are interesting.

"Numerology" generally refers to the mystical or occult significance of numbers or computations.

But "look how my formula is nice" questions are also off-topic, in general.

Well find a better name for the tag and tell me. I like the name numerology, it is fun and easy to remember, and the tag description can explain what it means in this context.

@reuns But that's not what numerology means!

Imagine the OP searching for patterns in weird sequences/formulas when there is essentially nothing to find? This is numerology.

No.

Numerology deals with the occult.

It is totally off-topic.

Kabalah is numerology.

Looking for patterns is not necessarily off-topic.

(though it often is)

(I think it's not possible to construct a set of all numbers if one includes cardinals. There might be a problem if taking the power set of all numbers or even only all cardinals and then Cantors theorem contradicts that etc. Anyway, the question was poor formulated but still thanks for sharing your thoughts.)

@vitamind Dr Baez had a series of blog posts about this...

er... maybe.

Or maybe he was talking ordinals?

But the same basic problem applies.

johncarlosbaez.wordpress.com/2016/06/29/…

@vitamind Don't fret it! It was a good question.

@amWhy It was just a question that popped up in my head out of nowhere :D. In the end I couldn't even define a number haha :).

@XanderHenderson I completely forgot about ordinals. I wonder if it's possible to rigorously define a number which is not an ordinal or an infinite cardinal (or any other number of the same concept). Probably (not) ?