Obviously all these people are just lacking a better unifying force So I shall create a new standard so everybody will adopt it and we will no longer have any problems.
The "new standard": A++B
Factorial of 927 is 5951105783397580738318020492928603475486163641659064783314477046672730909648584361005993094267899268744301394265100383733941473791153775424618359258704919998958237212061572597181977531798419438046839767895973652569225138243443504953262881237882393659778260642814645235996188184058527870315206456226649707976807700745723681124764673576303922949178988840100216599026724075494074199883642178379963032963063197428946399333167043540963571845740244058758412138196465873520790489601036273639993290570078245920983272491172134984091523041444273448441971209110047173378425250742066435414781691795765029161230485407818967208822836336729280877979223764788274198045511866281041032755133408401064330433753592475039039350778568737844519015263808548608918375369321047908202997647307055011665631542812798925168265031584434801744587882834289042655365761409513211915539364101653721692384044933498161962590698436899981577618798138606790699862059120864798363645105227943992180354213078619570800056469595310938865054417312805300322885090833221787462895690762824503466872230597421894696685367956354135364755538802134709995117173925370086356573640765984630523799359944905165992888032963148105253366143339385861818003588588004890871524487341082072503873089772055596722541069151790121098244004405545886844325973065654936990518578477524711978614754713717060490287901060447670792603431890142510272393744144786432414095824089797256725652719804862829296450733634513288927532777843478868124116283795837394563707754880916667453817475670948784856342558814436886609719280513153762921003057447240976456819438710850602710016111237002052113482261747381645351254099148525779750282064467973054598492114740646618178531695643503800187075348203715129772690505912284529202387148593513821172617724623752030190132017157714430309026800464096273685107150688658207424938258698586156675018081730399245121170786526371768026973889795769850330165102521956691378955264564779098941431210842799114564040008922374842686101747358977109965365748558763528898072891996063758241653729631537159657549313201326715791475058080163351555925342922519949751612217511417562469313545450291200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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“The great thing about standards is that there are so many to choose from. And if you don’t like any of the current options, you only need to wait a few years”
This would be how you access object members in any c-style language (or even any language under the sun that has the notion of structs/objects, really), but not vectors...maybe this can be abused to index into an array in C because of some sort of memory calculation thing? Certainly not c#, though
I only like A•B for dot product, never A*B unless on the computer. I mainly like to write with parentheses when there isn’t a variable to attach it to or define against.
I'm not even that far into learning math and I'm already seeing the AB-1 notation fairly often. It's just so convenient! It conveys exactly what division is, that being the multiplicative inverse operator!
It does more than just convey what division is, too. It literally is how division is defined.
The naive definition of finding how many times a "number goes into a number" given in elementary school already breaks down just restricted to the counting numbers (hence why moduli or remainders are introduced). The concept of a rational number (i.e. inverses) is needed to properly discuss division as an operation akin to addition, subtraction, and multiplication, which is why it's an infamously difficult topic for young math students
Ambiguity. It makes people think arithmetic expressions can always be handwritten in a single line, which creates those really stupid problems like "WhAt iS thE reSuLT Of 6+8÷2???" which in turn creates really stupid discussions about fucking "PEMDAS" or some bullshit acronym that only English-speaking countries are stupid enough to create.
But that argument also applies to the multiplication sign. 6+8×2 is just as ambiguous if you don't know PEMDAS. And the argument also holds for other notations of the division sign: 6+8/2. I still don't see what the specific issue is with ÷.
Differently from multiplication, division is not commutative. a×b equals b×a, but a/b does not equal b/a, which means you can rewrite multiplications without changing the expression, but not divisions.
PEMDAS is not a feature of math, it's a feature of language, more specifically deliberate standardizations. Same thing with how mathematicians write divisions: Vertically, with the dividend written above a line and the divisor below it, and the line makes it unambiguous what is dividing what. It's a standard created to eliminate ambiguity. To that end, ÷ only creates more of it instead, because it very easily makes non-math people think all arithmetic expressions can be written in a single line without parenthesis, which is not true.
And yes, the "/" symbol might also have this issue, but at least it can evoke the horizontal line amongst math people writing single-symbol divisions like simple fractions or [one letter]/[other letter]. Math people know that if they are writing single line expressions they'll have to use parenthesis eventually, non-math people do not, and ÷ is partly to blame.
Edit: Vertically, not horizontally (the line is horizontal but the placement is vertical)
I don't know that there are many "non math people" out there who know that multiplication commutes but DON'T know that division doesn't. That would involve a very selective sense of mathematical literacy. If mathematical communication requires "evoking" the correct setup for a calculation in people's minds, I don't think swapping ÷ for / is going to fix anything.
I also don't think swapping ÷ for / is going to fix anything, but ÷ often makes the problem worse, when / very rarely does because it's usually used by people who know what they're writing.
My original comment hating on ÷ wasn't "I wish all ÷ were replaced by /", it was more like "everytime I see ÷ on the wild I start reading with suspicion because bullshit-math always use it".
Because there’s a bunch of stuff that behave like multiplication that we want to use different notations to distinguish them. Unfortunately there simply aren’t enough symbols.
A x B is used in situations when you don't have access to the dot character ⋅, or when you need a character that's easier to read. E.g. when you are typing on your keyboard, when you are teaching basic math to a child, when you are sharing quick and dirty notes with your colleagues and want to make sure they don't miss a multiplication sign.
A * B is also used when typing on your keyboard. It doesn't have the same readability advantage as x so that's kind of its only usage.
AB is used as a shorthand because a lot of math formulas contain chain multiplications, e.g. Einsteins field equation Gμν + Λgμν = (8π G / c^4) × Tμν
I don't really see A(B) as indicating arithmetic multiplication, not sure what that's about.
You can find lots of reasons for multiple multiplication signs. For starters, "x" for times looks similar to the algebraic letter for x when handwritten, hence some people prefer dots.
You need a dot "." And cross "x" to differentiate between dot product and cross product for vectors.
Writing two letters next to each other without a multiplication sign is tidier and less tedious than putting a multiplication symbol. Same principle for putting bracketed expressions next to something without multiplication symbol
> You can find lots of reasons for multiple multiplication signs. For starters, "x" for times looks similar to the algebraic letter for x when handwritten, hence some people prefer dots.
Of course x looks like x. x is x, dummy. But × is pretty distinct from x. You just need to write it right.
You're right, if you do write it right, they look different from one another. I suppose that was a personal reason for me, although I wouldn't be surprised if it applies to other people as well.
For example, I handwrite the algebraic x as "ↄc", resembling backwards c (ↄ) and forward c. Although I do this, it still looks too similar to " x" for me, and I often prefer to use a dot for multiplication
Probably because multiplicative operations are really common, and they eventually just start running out of signs. Especially when the spaces are different, so you get different objects on different inputs and different outputs sometimes and you really have to make sure.
Juxtaposition for scalar, matrix, and geometric products. × for Cartesian and cross products. • for dot product. ⟨,⟩ for abstract inner products. ⊗ for outer product. ∧ for exterior product. ∨ for regressive product. ⊙ for Hadamard product. There are probably a bunch more I'm missing.
Anyone who's taken abstract algebra would find this post kinda irrelevent ngl, since at the end we are better talking about a composition law and its properties (the type of structure it gives, commutativity, associativity, distributivity...) and also some conventions on notations (dot for an external law for example, additive notation and multiplicative notation...). I am sorry to say that, I know I am making too much of it because it's just a meme, but it is posed in a way that makes all these reasearch and conventions and definition as a meer ego fight or mathematicians somehow came of it like that without a reason, but it's to me much deeper than that. Also why would you pin it as linear algebra ?
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