Post #4328570

@SmartmanApps@dotnet.social surely you understand that the interpretation of a given string of symbols depends entirely on your definitions, and surely you can admit that while we are close, we don't have a global standard for these definitions. Even if there was one global standard for order of operations and definitions, people would still be confused about 1÷ab, as you rightly pointed out with your example. And yes, they would be wrong in such a case, but that doesn't magically make the source of confusion go away. The reason I say that fractions make things clearer is because their scope is entirely unambiguous. To write a fraction you are forced to indicate its scope in its entirety, whereas with ‘÷’ we need to indicate its scope by relying on brackets. It's true that fractions are difficult to write in many contexts — though they *can* be written on a single line without brackets, if we use #LaTeX for example, or if it's manuscript. I don't think it's a coincidence that in the majority of maths papers where division is a relevant operation, we tend to see fractions and not division operators. If we really did want to use the division operator — for whatever reason — I would suggest that we use the form ‘((φ)÷(ψ))’, where the brackets leave no room for confusion (however misplaced the confusion may be). This could be excepted in the case where φ or ψ are atomic expressions, since then there is only one way to interpret the order.