Post #4339964

2026-08-02 12:25 UTC

@SmartmanApps@dotnet.social while I look for such an example, I'll leave you with this to ponder: https://en.wikipedia.org/wiki/Order_of_operations#mwyA ‘There is no universal convention for interpreting an expression containing both division denoted by '÷' and multiplication denoted by '×'.’

Replies (1)

@bemmesr@mathstodon.xyz 2026-08-02 14:59

@SmartmanApps@dotnet.social I have been looking for the textbooks as you requested. I've found numerous sources which say that there is such a discrepancy, though I have yet to see actual examples of it. Meanwhile, while I continue to search, I'd suggest you read https://math.berkeley.edu/~wu/order5.pdf as it essentially makes the same argument I'm making, perhaps with more clarity and conviction. It's not an uncommon idea. In ‘Mathematics From the Birth of Numbers’ by Jan Gullberg, on page 122 under ‘Operational Precedence’, Gullberg says, ‘we also note the left‐to‐right rule of precedence for multiplication and division: 24/2×6... but as this principle of precedence is not universally respected, we recommend, for the first case: (24/2)×6...’ Now, this has turned out to be somewhat of a research task, so I'll at least give you that there are not *many* textbooks published in the last 150 years which differ on the order of operations, but I won't yet concede that there are *none*, since of course we have no reason to believe this to be the case. I'd also like to add that the reason I say that the order of operations is arbitrary is because arithmetic is essentially just an axiomatic system, and of course the interpretation of a given sentence in such a system depends entirely on your definitions and axioms.

Open ##4339963