Glyn Wolf 
@glynwolf@tiggi.es
🏳️⚧️ No LGB without T! 🏳️⚧️ No pride without BIPOC! (P.S. 
💘 
4 ∞) I'm a middle-aged #greymuzzle, a #gamedev, a #gay cis-male, and a fan of #photography, #scifi, #fantasy, #LEGO and #rocketraccoon. A former near-life-long Albertan, I've just moved with my mate to start a new adventure in Montréal. J'apprécie toujours d'avoir l'occasion de parler français et de découvrir la culture francophone. http://nwac.ca
tiggi.es
Replying to
@FishFace@ioc.exchange
@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.
