Post #4436508

2026-08-06 14:43 UTC

@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.

Replies (1)

@FishFace@ioc.exchange 2026-08-07 08:35

@glynwolf@tiggi.es @IceWolf@masto.brightfur.net but left associativity is itself a notational convention. It's not a fundamental property of division: you can't prove that the division operation has this property, you have to decide you're going to follow the convention, and could choose not to. Furthermore, left associativity does not help you in a mixed expression like 12÷3×4. The author is using a nonstandard definition of left associativity and if you look it up on Wikipedia or in a textbook you will see it gives you that a÷b÷c = (a÷b)÷c, but doesn't say what to do when you have a multiplication instead of a second division. In our schooling, left associativity of division is a consequence of our order of operations conventions which say directly to do multiplication and division in order from left to right. If you do this with a÷b÷c you can see you immediately get (a÷b)÷c! Examples where this order is not chosen include: * Reverse polish notation * Calculators which evaluate strictly left to right (used to be the only way calculators worked) * Strange programming languages like APL * Dutch classrooms until they agreed to use the more common order (they used to do multiplication before division) If left associativity were an inherent property of division, none of these would actually be capable of doing division, yet somehow they are.

Open ##4436507