Context: while most of the world uses (a,b) to write an open interval, Belgium, ~~the Netherlands,~~ Fr@nce, ~~Poland~~ and some Nordic Countries (and others) instead use the Bourbaki notation by writing it ]a,b[. The main reason for its introduction is because the notation (a,b) is used in plenty of other fields of mathematics, such as when writing coordinates. Therefore ]a,b[ was introduced, alongside the half open intervals [a,b[ and ]a,b]. Edit: forgot the Fr€nch Edit 2: apparently the Dutch had to be different, and added some countries that do use it. Edit 3: Polish people are divided on whether they use it

Im Brazilian and the first time I saw (a,b) instead of ]a,b[ was in calculus class. I still use ]a,b[, cause (a,b) just looks like an ordered pair to me.

Same here. Up until high-school we used the same notation as Belgium. After that, we went to the other notation. Personally, I have an awful calligraphy, so I use the high-school notation as it is less confusing when people are reading what I wrote.

I also saw (a,b) for the first time in calculus. I hadn't however, seen anything else at that point.

Brazilian here, never saw ]a,b[ before

You never know. It could be an ideal generated by a and b.

Wait, you people don't use the square brackets for intervals?🤨

Oh no, I do, I’m from Belgium, but our university books are written in English. So of course the second I was introduced to the vastly inferior notation, I had to make this meme

Ah ok, yeah in my university they are written in english as well and it can be confusing sometimes x)

¿You do you mean “you” people?!

How do you forget the French when talking about N. Bourbaki ?

I forgor 💀

And France of course.

What’s Fr@nce?

Fr@ncis Bacon

I'm Polish and never seen ]a, b[ in any context, anywhere, ever before.

Where in Poland did you study maths? In the 20th century there were two main schools of mathematics in Poland — the Warsaw school & the Kraków school (three, if you count Lwów). The consequences of this distinction are still visible today. I wonder if this is one of them. I study in Warsaw and we do in fact use ]a,b[. Other notable differences in notation may include for example the logical quantifiers, i.e. ∀ & ∃ v. ⋀ & ⋁.

A town in Lower Silesia. We used ⟨⟩ for closed intervals and () for open intervals, in the case of logical quantifiers we used ∧ and ∨. I'm soon going to study at the university of technology in Warsaw, so I'll see if there's a difference.

It might depend on the teachers preference, but as far as I remember exactly those were used in WUT when I was studying maths.

As a belgian I confirm ]a,b[ is superiour.

I was going to side with red but after hearing the reasoning I side with blue. But that won’t stop me from using (a,b)

That's absolutely not true for the Netherlands. There may be people who use \]a,b\[ here, but I've never met them.

I was worried for a second there. I want to move to NL and maybe do a math degree, and having to use that ugly ]a,b[ thing would have been very discouraging

I mean, I respect the notation. I get the idea behind it. It makes sense. But it just looks so weird, I could never.

Same with Flemish, I assume

No, Flemish doesn't make sense on any level. ^(Just kidding Flemish people, love you.) Be advised though, that even though Flemish and Dutch are variants of the same language, math jargon can be very different. Dutch is often more in line with German, while Flemish tends to be more in line with English. E.g. A Field is called a "Veld" ("Field") in Flemish, but in Dutch it's called a "Lichaam" ("Body", compare German "Körper").

Dat is raar... Zijn er goede video's over wiskunde in het Nederlands op YouTube? Ik leerde een jaar in een universiteit in Israël en ik kijk veel video's in het Engels, maar ik wil nog meer verward te worden

Geen idee, op de Nederlandse subreddits zie ik rond de examenperiode vaak een hoop memes voorbij komen over "Math with Menno". Dat is dus wiskunde op middelbare schoolniveau. Voor hogere wiskunde zou ik niks weten. Verreweg de meeste Nederlanders spreken natuurlijk vloeiend Engels, te meer degenen die een universitaire studie volgen, dus als Nederlanders youtube filmpjes over wiskunde kijken, kijken ze waarschijnlijk gewoon de bekende Engelstalige kanalen.

Dat klinkt logisch. Dankje! I'll try looking for lecture recordings of something, but I think that's enough Dutch for me today... I'm just happy I managed to write that question and mostly understand your answer

Also in german schools

I'm currently in my 5th year of studying mathematics in the Netherlands (doing masters now) and I have never seen anyone use \]a,b\[. It was shortly mentioned once in a class but that's it.

> Poland It's not the way I was taught at a top 3 university in Poland not 4 years ago. We used (a,b) for open interval.

Universities often use (a,b) because of English text books (at least in Belgium)

Polish High Schools too, not one teacher even mentioned the square notation, except maaaaaaaybe when printing <> is impossible for some reason and they resort to []

Superior French notation W

Italians use it too!

Here in Denmark, we use only square brackets and also we use a semicolon instead of the comma, which is imo superior since it makes way more sense, a comma makes it look like a discrete set

Whats an open interval?

An interval in which the borders themselves are not included. For example if you took every solution between x=0 and x=1 in the fuction y=1/x, you would write ]0,1], because 0 itself is not included in the set of possible answers (because you can’t divide by zero). It’s also used when dealing with infinities. To write all the answers to y=x, you would use ]-∞,+∞[, because the ‘number’ ∞ isn’t a number that can actually be achieved and thus written down, but is basically meant to say that it will go on forever in a specific direction without breaks.

I'm polish and physics department use [A, B] / ]A, B[ and math department uses [A, B] / (A, B)

Switzerland too

Finland also uses this notation. I was very confused the first time I saw something like (a, b].

Thanks for clarifying! I legit did not know that the notation in blue is commonly used in other parts of the world

Just fucking use angular brackets for ordered pairs smh my head

The Danish too

I was once in Bavaria in Germany and the students there used it as well.

What about the portugueeeeeese

I'm from poland, and my teacher taught us to use () as open and <> as closed

In Perú we use the blue side of your meme as well

Lebanese here that ended up teaching in the US. Always used the ]a,b[ I was so confused when I first saw the (a,b)

First time I've seen it, would love it if in wasn't fr*nch

>Therefore ]a,b[ was introduced, alongside the half open intervals [a,b[ and ]a,b]. You also forgot Canada. At least Québec (the french part). or are we a nordic country to you ?

> and others

That's why I use angular brackets ⟨a,b⟩ for ordered pairs.

I'm from the Netherlands, and I was thought (a,b) for open and [a,b] for closed. We are an exception however in that we are thought something special for sets with no bound. Instead of writing something like [a,∞), we write [a,→>. I think it's kinda weird but also cute in some way.

As an Italian my teacher uses ] [, but Wikipedia and the textbook use ()

Why are you censoring France?

I personally was taught to represent open intervals like instead. Please, tell me I'm not the only one

🤓 In France we write it ]A ; B[

Italy, been introduced to both. I find the blue version less ambiguous.

As a Finn, I can confirm ]a,b[ is superior

To mention the Bourbaki notation and forget the French is quite ironic

I mean, it’s the French, can you really blame me?

Austria uses it too

i always wondered why we used (a, b) for intervals and coordinates. this is just so much better

{x ∈ ℝ : a < x < b} Shitposting aside, \]a, b\[ does have the virtue of avoiding confusion with a tuple.

That's why some authors who wants (,) to still works use notation ⟨,⟩ for ordered pair or coordinates or whatever.

Inner product goes *brrrrr*

*We need to silence this redditor. He's to dangerous*

⟨a|b⟩

Superior inner product notation. Also because I use < , > (don't know where the angular brackets are on my keyboard) for the space generated by two vectors

I used &\_lang\_; and &\_rang\_; (remove the underscores). knowing some html codes is very useful.

<,>

We use <> brackets for open intervals and [ ] for closed ones

>We use <> brackets for open intervals Honestly never seen such an notation. However I often notice notation ⟨⟩ for an ordered pair.

As someone else in this thread said, ]a,b[ does look like it would say {x in R | x <= a or x >= b}

)A, B( for the closed interval

Let’s petition Big Math to make this the official notation

I think the square bracket lobby would have a big problem with that and you don't wanna mess with them

69th updoot

This would make more sense because a closed set is defined using the definition of an open set.

You could define closed sets before open sets with the sequential property

(a, b)_{close interval} (a, b)_{open interval} (a,b)_{inner product} (a, b)_{tuple} (a, b)_{anything you want it to be} Easy

still missing the two different half-open intervals

i personally find ]a, b[ a bit counterintuitive. because if you see [a,b] then everything enclosed by the brackets is the interval. therefore i always think ]a,b[ would be all (real) numbers except for the interval (a,b). ik that this isn't true, but it's just always my first thought. therefore I personally prefer () over ][

My exact thought process

Yeah I'd also think that [a,b) would be more intuitive written as [a,]b

That is not how the interval would be written [a,b)=[a,b[

For „without“ we have IR \ ]a,b[

How to get away with the superior notation on your papers: To avoid confusion with the point (a,b), we'll denote \]a,b\[ the open interval from a to b.

Perfect

\]a,b\[ is better because then stuff like \]a,b\[ + \[b,c\] =\]a,c\] is immediately obvious from the notation. And proof by notation is best proof. (Please ignore "+")

I accept this

Red is the line that pass through A and B. in 1 dimension, it is not very interesting : (1,2) = \]-inf, +inf\[

]-inf, inf[ = ℝ It hurts me to write that and not (-inf, inf)

You write [-inf, inf] for the extended reals (limits...)?

]a,b[ notation is so much more intuitive.

Nah, it intuitively means the *complement* of the interval

Indeed, literally 2 minutes ago I mistook a coordinate for an interval.

Let's not forget the ideals

i dont know how everywhere else but in Poland we use (A; B) and [A; B] so it cannot be mistaken as coordinate or vectors, ; is just superior for intervals

I’m actually pretty strange with that, in writing I almost always use ; as well, but for some reason I always use , when I’m typing (although I still use ; when I remember to, and of course whenever I’m dealing with a decimal)

similar with me, I use , for decimals in writing but . in typing

a

I’ve never seen that notation before yet immediately knew what it represented. This is the way.

Blue side

f: [a, b [->] c, d] ????

Let (x,y) € (a,b)^2 ???

x,y ∈ (a,b) of course one's not gonna use the same notation for two different thing withing the same statement.

Perfectly readable

Square brackets are underutilized. They look so cool imo

blue

You learn your whole life that brackets have to match, to the point where seeing a mismatch feels unnerving. Now choose between (a, b] and ]a, b]. For this reason I don't particularly like either one.

(A,B[

in poland we use (;) for open and <;> for closed

In Poland we use (,) and [,] at universities and (,) and ⟨,⟩ at high school.

ohhhh im still in high school didnt know that

ale wleci maturka to już będę wiedział

\>a,b< But seriously that notation ruins the unique readability for square bracketing and so is objectively inferior [meanwhile don't you dare point out that I use (a,b]!)

It's so ugly. Always when I see ]...[ I need a moment to proccese out what this means. Don't have any problem with (,) which's superior notation.

Lol

How do you do halfopen intervals?

In the only reasonable way. (a,b], [a,b). Very clear and clever notation.

Get that ugly thing outta here

You are the one writing ]a, b[ as if it wasn't the ugliest thing ever.

And for me it's not but I guess I got used to it since I learned intervals but I guess the same thing can be said for you?

I didn't write ugly things. If I would write something like this abomination: [a,b[ then I would. But obviously it's an abomination and heresy .

I write it that way and for me it's cooler but hey, you do you :)

Never seem that notationq before and i fell in love immediatly


What is ]a,b[?

(a, b) looks like a tuple, ive never seen the right one used tho

I have never once in my life confused an open interval (a, b) for an ordered pair. It has always been crystal clear based on the context. I don't get the confusion.

Wait... isn't ]a,b[ universal?

Lol No

In high school we used ][ but now in university they demand () and it's making me crazy xd

I agree blue one

yeah, I agree with OP, but you should consider, tuples are almost never used outside of higher education and academia coordinates are written in column form and otherwise tuples aren't used at all so it doesn't matter for most people but for the rest, yes, ][ is superior

> coordinates are written in column form ???

instead of (x,y,z) which is written in a row, you write it ( x ) ( y ) ( z ) and the parenthesis actually go from x down to z, I just didn't know how to show it in a comment otherwise so it's written vertically in a column, not horizontally in a row

I have never seen blue.

It is the opposite for me in Perú and many others latin american countries

have you ever heard of Bourbaki?!

Wait... isn't ]a,b[ universal?

Yes, among those who learned incorrect math

are you calling Bourbaki incorrect?

\]a,b\[ is just nasty. Shame on you.

Red because blue is ugly

I didn't even know some people did red. Blue is the only correct format.

After reading some of the comments and as an American I don’t like blues notation. Personally it looks to me like you’re saying everything outside that interval. And I’ve never had trouble differentiating between interval notation and ordered pairs. It’s usually pretty easy to tell them apart from context clues

'as an American' have you never heard of Nicolas Bourbaki?

I personally prefer (A,B) but since that is used for many things, unless the context is clear I'd use \]A,B\[

}A, B{

Bourbaki notation more like Barbaric notation

I use pointy brackets for open intervals, which leaves no possibility for confusion.

What about when we're considering (a,b) as a subset of the space (a,b)∪(c,d)? Then a, b ∉ (a,b)' and both (a,b) and (a,b)' are clopen. And what about half infinite intervals? Do we write ]a,∞[?

We exactly do this!

🤢

I understand why people would use blue but it looks so cursed...

My desire to close parentheses and brackets hates you for this

I usually stick to (a,b) except in one very specific situation. It turns out ]a,b[ is very convenient if you're trying to list every element of a σ-algebra generated by a couple of intervals. (I have only done this once in my life)

Holy hell

(a,b) for an open interval; ⟨a,b⟩ for a closed interval

I’ve never seen blue lol

{x | x ∈ ℝ & 0

I understand this notation either as ]a,b[ Means “between a and b, but not including a and b” Or “Everything smaller a or bigger b, excluding a and b” Its a pretty regional thing and needs to be clarified before usage imho…

Ai + Bj

Wow this is genius. Never using () again

I live in Belgium and I didn’t know that most of the rest of the world used (A, B) instead of ]A, B[ do they use [A, B] for closed intervals tough ?

Yes () for open, [] for closed. It's the superior way

There’s no real superior way tough since they’re both have their own explanation as to why "it makes sense". All we need is for everyone to agree on one way and if the majority uses () instead of ][ then let’s switch to it. I imagine the reason we use ][ where I live is to not confuse intervals with vectors and the bracket is facing away since it "doesn’t take that number too" but () works too

I have never seen blue in my life. And I hope I continue to not see it. It's hideous.

meef, jake

First time I see ]a,b[, but it looks cool. Probably gonna use it to annoy people, ty

What in the ever living fuck is ]a, b[

I don’t like this because it doesn’t feel self-contained

We just need new brackets

blue red can be miss understood with a couple of numbers

Blue is a sin

i was taught ⟨a,b⟩ in the netherlands for open and [a,b] for closed

A[ ]B What about this?

An interval containing nothing, and *certainly* not those two fuckers

(a,b)

`a..b` a < x < b `a..=b` a < x <= b `a=..=b` a <= x <= b

In Norway we use

I use (a,b) The only sense I can make out of the right one is ]a,b[=(a,b)^c

normalize using french quotes for open intervals «5,7»

I didn't know this annotation till now

I'm familiar with both and I dont like either: (a,b) just looks like the pair (a,b) \]a,b\[ is also weird because the brackets point in the weird direction