this post was submitted on 19 Jul 2023
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It is, in fact, completely arbitrary. There is no reason why we should read 1+2*3 as 1 + (2*3) instead of (1 + 2) * 3 except that it is conventional and having a convention facilitates communication. No, it has nothing to do with set theory or mathematical foundations. It is literally just a notational convention, and not the only one that is still currently used.
Edit: I literally have an MSc in math, but good to see Lemmy is just as much on board with the Dunning-Kruger effect as Reddit.
If you don't accept adding and subtracting numbers as allowed mathematical transactions, multiplication doesn't make sense at all. It isn't arbitrary. It's fundamental basic accounting.
What you just said is at best irrelevant and at worst meaningless. No, the fact that multiplication is defined in terms of addition does not mean that it is required or natural to evaluate multiplication before addition when parsing a mathematical expression. The latter is a purely syntactic convention. It is arbitrary. It isn't "accounting."