OK, I found this post on Tumblr and I understand *nothing*.

nonanalogue.tumblr.com/post/18

The purpose of the mathematical language is to be non ambiguous. How does this work?
For me, the post concluding this thread is obviously wrong. Are my math just super rusty and I should be ashamed, or are people in France and in the USA not using the same notation?

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@Sylvhem to me the main problem is that people are taught different thing, and not how it's written. PEMDAS and what we learn in France (* and / on the same level and before + and - that are also on the same level, left to right) gives different results so it's confusing

What I wanna know is why we're taught different stuff over different countries :')

@Sapphaos Thank you! That's where I was trying to go with this post in the first place ^^'.

@Sylvhem yeah everyone in the answers is going in a different direction but it's not written in a confusing way at all. If I had that on a test, I would write 16, my teacher would probably expect me to write 16 on my test :/

@Sapphaos Exactly! Thank you, that was exactly what I wanted to express.

@Sapphaos @Sylvhem The issue, really, is that pedmas is a lie. If an operation obeys the associativity priniciple. That is, for the any 3 objects a, b, and c: (a `op` b) `op` c = a `op` (b `op` c), then there is no need for parentheses and the expression can umabiguously be written a `op` b `op` c. When you start mixing operations, however, this relation can fall apart and parentheses are needed. And some operations, like the division sign given, this doesn't hold and parens are always needed.

@Sapphaos @Sylvhem Actually, this is true of any inline division. Take the expression 6/3/2. Taken as 6/(3/2) it is 4. But, taken as (6/3)/2 , it is 1. That is, division (written this way) doesn't associate ((a/b)/c != a/(b/c))

@Sapphaos @Sylvhem This all falls away, however, when you replace the (ambiguous) division with multiplication by fractions, since multiplication does associate. 6(1/3)(1/2), which is unambiguously 1 no matter how you evaluate it

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