@EliahKagan I don't seem to understand this at all today. I thought it might become clear overnight (as often happens) but the reverse happened

Embarrassingly, I don't fully understand this notation. I should go and read about that

@EliahKagan haha I would think your first statement was right,... but this makes me think of how recently I noticed that people were making statements about their country or region that directly conflicted with statements made by other natives of the same region or country about the same things, so I have tried to start being more tentative in my own statements, saying qualifying things like "in the dialects of English I am familiar with..." or "in my extended family..."

But sometimes it seems that people then feel, possibly rightly, that I am saying something that fails to address the topic in hand

or fails to say anything of interest XD

today is a major festival here and it is making me feel lonely

I have been privileged to visit New York (City) twice

@Kulfy finally this week, after many attempts, I succeeded in making stuffed aloo paratha (I say stuffed specifically, because while struggling with that I made it a cheating way, by incorporating boiled potato and other stuffing ingredients in the dough itself)

@Zanna I just shifted to Pune to work as an intern and all I'm getting is Sambar 😑

Although Pune is in Maharashtra. Sometimes I miss North Indian cuisine.

well obviously here in TN sambar comes with every meal

Yeah I can expect that in TN but not in Maharashtra.

I found food here spicier than what we have in North.

yeah I would have thought it would be all pav bhaji & vada pav

my favourite dal is apparently from Maharashtra

amti

it is a bit like sambar because it's tur dal and has tamarind

but it has that amazing goda masala with sesame and coconut

@Kulfy do you like spicy, or no?

I need to go out of my apartment to have "real" Maharashtrian food.

I could definitely go for more spicy than the food here. The only thing spicy on the leaf in the places I go to is pickle

@Zanna Yeah I do.. But it's too spicy here.

They add too much garam masala

ooooh I hate it when the food has too much garam masala. Bitter!

why are you only getting sambar anyway? From your workplace?

I'm having mouth ulcers because of that 😟

PG?

Yeah.

@Kulfy you must eat fruits. You need vitamin C

There are so many south Indians here. May be because of that.

@Kulfy sympathies :S

No time to cook on my own.

yeah :( very tough

@Zanna Yeah. will try to go market this weekend.

I hope you're enjoying your work and it will be useful for you

@Zanna The food is overall good and accommodation is also fine. So I guess I can survive here :P

@Zanna Yeah and thanks

I love sambar anyway. I can happily eat sambar every day. But not with garam masala in it XD

In north we have coriander leaves for everything. But here dal is incomplete without curry leaves or "Meetha Neem"

here too. But coriander is also used.

You know, I have a slightly funny story about curry leaves

Umm what?

I absolutely love them, but in UK, they are very rare. You can buy from the supermarket a little plastic cylinder with about 15 dried up curry leaves in it for the equivalent of, say 200 rupees

and dry curry leaves don't have much flavour anyway...

just before I came to India in March, I found that the luxury supermarket in the county town of my region was selling fresh curry leaves

you get 2 sprigs of them for something like 250 rupees

I tasted them... wow! so much better than the dry ones

Then I arrive in TN and curry leaves everywhere. Bliss.

After a few months I get my apartment and kitchen and start cooking

I go to the fruit & veg shop...

I wanted to buy curry leaves... so I added to my basket of stuff three small sprigs of the stuff from a huge pile by the door

when the guy who served me weighed my stuff, he clearly did not see my curry leaves. It was obvious they did not exist for him. Just a bit of debris that fell into the basket accidentally. He helped me to pack, deftly chucked the (to him) empty basket on a pile behind him and said "forty two". I pointed at the huge pile of curry leaves to his right. He pulled off a fistful of sprigs, about 3000 rupees worth back in UK, and put them into my bag. No further charge was applied.

Whoa that's way too expensive. Have you considered growing a plant in your house?

that's my version of "culture shock"

@Kulfy in UK?

Oh well that won't survive in colder regions I guess.

@Zanna Yeah.

yeah maybe it would not grow in our climate... yeah the price is outrageous

but here curry leaves are free

@Kulfy is it "sweet neem" you call it?

Yeah. In north India coriander leaves are free but curry leaves aren't. But that's ain't that expensive.

we have to pay for coriander leaves, but not much :)

@Zanna Yeah at least in my hometown in north.

I think that's a proper name... it is related to neem I think

Yeah and the bark can also be used as a replacement to toothbrush and toothpaste. In north we called it as daatun. No idea what it's called in South or west

daatun literally translates to a thing for teeth (daant)

awesome. I had no idea about that

Neem also purifies blood if 2-4 leaves are chewed in the morning before having breakfast.

When I was a kid daatun was very common in Northern areas also. But then Colgate took the market

when I walk around the streets here I feel that most of the things growing are things that are used by people, like coconut trees, drumstick trees, neem trees, turmeric and carom plants, banana trees

@Kulfy I didn't know that either, but I notice it's used in toothpaste and soap and cleaning products as its oil is antibacterial

Once a very big personality said that the foreign toothpaste companies use things like neem just to please Indians. 🤷🏻‍♂️

Yesterday I read somewhere that there are more Indian hotels in London than Delhi and Mumbai. o.O

Lunch over. Gotta go back to work.

@Kulfy surely they adapt to local preferences. I see the same brands making different products here. Those toothpaste brands don't have neem or tulsi or whatever in UK

@Kulfy I have decided that the UK is, essentially, a region of India, with its own regional cuisine, because there are countless Indian eateries in the UK, and they serve a distinctive repertoire of dishes, some of which are obviously descendants of ubiquitous dishes like masoor dal tadka and chole/chana masala and what have you, and others which, while possibly based on some dish of some region actually in India, are probably unique to the UK...

of course, you can sometimes find a place serving some regional cuisine. For example the city where I stayed when I was doing my first degree, Leeds, has a very very nice veg Gujarati restaurant

and in London, one can find distinctively Bengali spots, and "South Indian" places like Saravana Bhavan and Sagar that serve dosa (with mint coconut chutney that tastes like toothpaste)

but that does not undermine my argument that the UK is a culinary region of India. Here in Chennai, we can easily find an Andhra mess or a hotel specialising in Hyderabad dum biriyani etc

still, I have not been around the place here, so my opinion is ill-informed.

anyway, it's easy to imagine why Indian (or loosely Indian-style) food is popular in UK. Indian food is just objectively way better than all the other food available in UK :)

@EliahKagan how do we set that up?

would be good to try learning

@Zanna ChatJax++ checks what site the room is associated with, and it uses that site's MathJax configuration. This has the benefit of avoiding the performance penalty for rooms associated with sites on which MathJax is not enabled, as well as giving a reasonable configuration (like, reasonable packages).

To make it work in a room associated with a site on which MathJax is not enabled, it should be sufficient to modify the code to special-case the room, so it is treated as if it is associated with a different site, or (perhaps easier) the site, so all rooms associated with it are treated as if they are associated with a different site.

Another option is to just use the original ChatJax user script, which I believe works in any room. But with that you have to click to expand TeX formulas; they don't render automatically.

@Zanna I can explain or clarify what it means and you can go and read about it. :)

However, I don't know specifically what notation you're having trouble with.

I mean this set-builder notation in general

@EliahKagan There are some disadvantages of using MathJax in here. It won't render if the necessary user script is not installed, including for example if you read this on another device, and on a weaker machine you will notice the performance penalty. It is for the latter reason, performance, that SE never enabled MathJax in chat.

@Zanna Oh. I can just go through the common forms right now.

that would be very nice

{x | Fx} is the set of all and only those x for which Fx (i.e., that satisfy the formula "Fx").

However, there is not always such a set.

For example, if Fx means x ∉ x, there can be no such set, due to Russell's paradox.

(In set theory, one typically only has the "=" and "∈" predicates built-in. Everything else can be expressed with them. As we talked about some time ago, you can even do without "="; you can define it with "∈" and quantification, so long as your axiom of extensionality is suitably modified. But in place of where I am writing "Fx", you can have a formula of arbitrary complexity. We don't limit ourselves to atomic formulas on the right side of "|" anyway.)

The "|" in set-builder notation can be pronounced "such that". Some people use a ":" instead of a "|". That means the same thing.

ok, all good so far :)

{x ∈ S | Fx} is the set of all and only those x in S for which Fx.

That is, {x ∈ S | Fx} = {x | x ∈ S ∧ Fx}. That is even one way to define this form of set-builder notation. Note that, whether or not any x ∉ S satisfies Fx, it is the case that {x ∈ S | Fx} ⊆ S.

(As before, Fx needn't actually be an atomic formula of that form, or even an atomic formula at all; it may be arbitrarily complex. We regard it to be parenthesized if necessary, to ensure "x ∈ S ∧ Fx" remains a conjunction of "x ∈ S" and another formula.)

@EliahKagan ok, I see that

(By "parenthesized if necessary," I do not mean that you can write things like {x | x ∈ S ∧ Fx ∨ Gx} and have that be meaningful, as you cannot. I mean merely that, if you define terms of the form {x ∈ S | Fx} as a special syntax for terms of the form {x | x ∈ S ∧ Fx}, then {x ∈ S | Fx ∨ Gx} would expand to {x | x ∈ S ∧ (Fx ∨ Gx)}. This is to say that you need not write {x ∈ S | (Fx ∨ Gx)}.)

So, that form, {x ∈ S | Fx}, may be regarded as a special case of the more general form {xRy | Fx}, where R is any infix binary predicate or relation. {xRy | Fx} = {x | xRy ∧ Fx}. For example, you can write things like {x > 2 | Fx} (though it should be clear precisely what ">" means when you do it). Not everyone recognizes this more general form, but that is not the main reason I did not introduce it first.

ok

Rather, there is something special about the form {x ∈ S | Fx} that does not apply to the more general form {xRy | Fx}. And that is that there is not necessarily any such set {xRy | Fx}, just as there is not necessarily any such set {x | Fx}. (After all, for xRy, we could write x = x, so the form {xRy | Fx} can express anything {x | Fx} can express, but whether or not there is any such set as {x | Fx} depends on what we put for Fx.)

In contrast, however, with the specific form {x ∈ S | Fx}, there is always such a set. The caveat is that we really want to be able to write a term of arbitrary complexity (not containing any free occurrence of "x") for S, and so long as that term succeeds at referring to an object, {x ∈ S | Fx} does too.

The reason sets expressed in the form {x ∈ S | Fx} always exist is that modern set theories adopt a weakened form of unrestricted comprehension, called restricted comprehension, or specification, or selection. Recall that, in Frege's system (but with modern notation), one could always prove that {x | Fx} exists, and this led to Russell's paradox, where x ∉ x is put for Fx.

The modern set theory solution is to not have axioms that strong--since that's so strong it causes one's theory to be inconsistent!--but instead to require that one start out with some set before carving out of it the set of all and only those elements for which Fx.

Another way to put this, informally speaking, is that modern set theories have axioms that all the {x ∈ S | Fx} exist.

ok

Given the {x ∈ S | Fx} form of set-builder notation, there is a mechanical procedure that can generate an existence proof for the set. This is because the theorem proved is always of the form ∃T ∀x (x ∈ T ↔ (x ∈ S ∧ Fx)). When I show precisely how restricted comprehension is axiomatized, it will become clear why the axioms are always sufficient to prove sentences of that form.

I would be interested to say more, since not all occurrences of set-builder notation take the above forms. However, I believe this is sufficient to understand the notation in that message. (Please let me know if it is not, however.)

now I understand the notation in the message just fine, but I still seem to not understand the message at all. If we add some things to S then it remains exactly the same...?

We're only adding things a for which ¬Fa.

but those things are not relevant

they are not part of the set we've described

which is some subset of S

Right.

ok, got it :)

I mean, S' is not a subset of S. It has some things in it that are not in S. But none of those things -- call an arbitrary one of them x -- satisfies Fx.

some subset of S can be the same as some subset of S'

In fact every subset of S is a subset of S', since S is itself a subset of S'.

oh of course :)

Do those messages make sense now? And do they clarify how n-ary relations do the work of n-ary predicates in the same sense that sets do the work of unary predicates?

yes they make sense, and yes that seems more clear

From earlier, other than the part you were referring to there, was there other stuff that did not fully make sense?

Regarding set-builder notation, another common form is {f(x) | x ∈ S}. I've written "f(x)" but the left side may be a term of arbitrary complexity. For example, {x * 2 | x ∈ ℤ} is the set of even integers (i.e., even numbers) and {x * 2 + 1 | x ∈ ℤ} is the set of odd integers (i.e., odd numbers). Another example is {x + 1 | x ∈ ℤ}, which is just ℤ, as for every integer there is an integer it is one greater than.

Another example is {x² | x ∈ ℤ}, which is the set of perfect squares of integers (which is usually what we mean by "perfect squares"). You will notice that this last example is different from the others, because more than one value of x ∈ ℤ lands on the same x², because a² = (-a)², but a = -a only when a = 0. It is still permitted.

@EliahKagan that part was ok

Any other stuff that was not?

Sorry, that very general. I just mean, was there anything you were unsure of, had a question about, or thought might have contained an error, that you had not gotten around to asking about, either because the conversation moved in another direction, or because you had hoped it would make more sense later but it did not?

$$\overrightarrow v = \frac{\mathrm{d} \overrightarrow r}{\mathrm{d} t}$$

^^ Testing ChatJax++. :)

sorry, I went out to buy some groceries

@EliahKagan the generalness wasn't unreasonable...

I am still re-reading

I'm not sure if I understood everything but, I try to keep asking about what I didn't understand

@Zanna That is also a thing that is not unreasonable! :)

:D

Before we continue...

ChatJax++, with appropriate modifications, does work in this room. Do you want to try it?

yes, sure

github.com/EliahKagan/chatjax

If you wish to audit the specific change made to the code: github.com/EliahKagan/chatjax/commits/master/…

The link that installs this modified version is the one in the italicized blurb at the end of the README (i.e., go to the GitHub page and scroll way down).

I was hoping you would tell me how to do it, due to my laziness, but you did it for me :D

You can also modify the script yourself, in your browser, if you prefer that.

this is good

@Zanna The TeX in the velocity message renders?

hmm... no

What's... good then?

haha it's good that I haven't done any work

Oh.

maybe it will work if I do something

Regarding it not working, do userscripts work for you in general? And have you reloaded the page?

userscripts usually work fine on my other system

but this is the first one I've attempted to install on this one

I have reloaded it and closed the browser and opened it again

How did you install the user script? I am assuming you used a userscript manager like Greasemonkey. Which one did you use?

I used Greasemonkey

it says the script is enabled

You're in Firefox, right?

right

If you press Ctrl+Shift+K to open the web console, do you see any messages that relate to ChatJax++ or MathJax?

hmm... when I press those keys, I get 4 spaces and nothing else happens

but I have this

ChatJax++ error: ReferenceError: "GM_getValue is not defined"
    userScript user-script:github.com/vyznev//ChatJax++:150
    userScript user-script:github.com/vyznev//ChatJax++:198
    scopeWrapper user-script:github.com/vyznev//ChatJax++:219
    <anonymous> user-script:github.com/vyznev//ChatJax++:220

in the console

Hmm.

That seems related. :)

yes!

Just to be sure, can you check if this happens in places where ChatJax++ is supposed to work without modification? It would be very strange if it didn't, but I still think it's worth checking. This message, even viewed in a transcript, will render if ChatJax++ is working properly. Navigating to that page and checking if it does, and what the console says, should be sufficient to check if this modified version of ChatJax++ will render it.

that message does not render for me

same message in the console

I did not expect it to work, given the error you got here, but I thought it prudent to check. Now I recommend then uninstalling this modified version of ChatJax++, then installing the original version, and verifying that the same problem occurs. I expect that it still will, but I do not want to assume that. If it does not occur, something is wrong with my modifications, though I don't know what.

If it does occur, then ChatJax++ may be incompatible with your browser version and userscript manager, or the combination of the two.

yes I get the same error, though with different numbers at the ends of the lines

hmm I have to go attend to some other thing

I'll try using a different userscript manager later

I think it will work with ViolentMonkey.

The different line numbers are because I added a few lines near the top of the script to document that it was changed, and because my modification adds a line or so.

I suspect that ChatJax++ does not work with new versions of GreaseMonkey and that the problem relates to How to make GM_getValue existent in GreaseMonkey on Firefox? It's not difficult, but would take a bit of time, for me to test this myself, because while I use Firefox, I don't use GreaseMonkey, because for unknown reasons I couldn't get it to work with FIRE.

(FIRE generally works fine with GreaseMonkey, so I don't know why I had problems with that. It's based on those error messages that I think ChatJax++ probably does not work with new versions of GreaseMonkey.)

@Zanna Btw, sorry. You have to click outside the textarea for that key combination to work. The web console can also be opened via menu > Web Developer > Web Console.

@EliahKagan oh yeah, neat! I just pressed Ctrl+Shift+C and changed to the Console tab

@EliahKagan I thought so

ok I installed ViolentMonkey and it looks like velocity is the change in displacement over the change in time

:)

cool :D

Have you used TeX before?

no, well I had a go at it once but I don't remember anything

I know there is a help page for it...

I'm going to misuse the word "math" because it won't cause the same sort of confusion as if I misuse words like "formula," "term," or "expression."

You might want to put math inline, in prose. To do that, surround it with single dollar-signs on each side. Let's see if ChatJax++ knows not to treat $ specially when the $ character is formatted as code.

It does!

:)

So, $\{a, b, c\}$ render as $\{a, b, c\}$.

In contrast, $$\{a, b, c\}$$ renders as $$\{a, b, c\}$$ even though it is in the middle of a message.

The { and } characters perform grouping for TeX itself, so to write them literally, as I have done, you must escape them with a backslash. Note that \ is not just an escape character, though. It is the first character of commands. (Technically, I think it might only be the first character of commands, and \{ is just a command that writes a "$\{$" character.)

For example, $x \in S$ renders as $x \in S$.

Detexify is the most useful tool ever.

I recommend trying to write some math in TeX.

I would consider this room good for that purpose, since it's an off-topic room anyway so it doesn't matter if it accrues a number of successful or failed TeX messages. :)

(Though I should mention, if you want to write actual documents, or you want to be able to test things out, whilst still using a webapp... I recommend Overleaf.)

Detexify is my go-to place when I have an idea of what something looks like (so I can draw it) but don't know how to do it in TeX. Even when that doesn't succeed, the page conveniently also links to The Comprehensive LaTeX Symbol List. If you were to use TeX while disconnected from the Internet, you'd probably want a local copy of that.

(Also, if you were to use TeX while disconnected from the Internet, you'd want to install an implementation of it on your computer. :)

I can show how all the symbols I've been using here regularly are written in TeX, but I'll hold off until you actually indicate you want me to do that, lest it hijack your more self-directed efforts.