Glyn Wolf

RE: https://dotnet.social/@SmartmanApps/117006976986454267 I love this post. The explanation thread right after the poll surprised me and made me think differently about what PEMDAS/BEDMAS/BODMAS etc. mean. It's well worth a read! 18 ÷ 3 x 2 is not the same as 18 ÷ (3 x 2) but not because of PEMDAS. It's because they're completely different expressions: 18 ÷ (3 x 2) = 18 ÷ 3 ÷ 2 NOT 18 ÷ 3 x 2 18 ÷ 3 x 2 is in fact a completely unambiguous expression that has only one correct answer, and the reason is not PEMDAS but the nature of division itself. The purpose of PEMDAS is just to help you avoid mistakes.

@IceWolf@masto.brightfur.net Did you read the explanation thread? I think it's very clear but I had to read it a few times before I grokked it. My post is just a teaser, not the full explanation.

@IceWolf@masto.brightfur.net You just need to read the original poster's 6-post thread. It's all in there. The key observation is that left associativity is a fundamental property of division. You can in fact carry out the multiplication and division operations in any order you like, so long as you constrain yourself to left associativity. e.g. 18 ÷ 3 x 2 = 18 x 2 ÷ 3 That's guaranteed because order does not in fact matter, so long as we respect the constraint of left associativity, as we must because division demands it. PEMDAS simply gives us a simple mnemonic to ensure that we always do.

@jepyang@wandering.shop I hereby nominate this post to win the fediverse!

@tisha Let us all remember the wisdom of Tom Lehrer: “Life is like a sewer: what you get out of it depends on what you put into it.”

@Blanche@piaille.fr Peut-être s’agit-il d’un symbole utile de la dernière crise ridicule de la masculinité?

@SwiftOnSecurity That is fucking evil! ⚡️

@FishFace@ioc.exchange @IceWolf@masto.brightfur.net Alright, let's see where this idea leads. We're sticking with the rules of algebra here and adopting the convention that division is right associative: a ÷ b ÷ c = a ÷ (b ÷ c) = a ÷ b x c We now have an algebra that is logically inconsistent. The convention of left associativity was not chosen arbitrarily. It is a necessity in the algebraic system as it's defined. I will grant you that my phrasing "a fundamental property of division" was misleading. What I should have said is that once you adopt the notation "numerator ÷ denominator" to express division, the rest follows as a logical consequence. The lessons we received on order of operations were not given to us to resolve an ambiguity, they were mnemonics to help us carry out the operations correctly. I'm not going to engage with examples outside of algebra such as RPN or calculators because those are completely different systems with different rules and goals. Once we step outside the rules of algebra, yes, I grant you, there are many ways to express math and computation.