this post was submitted on 19 Jul 2023
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Pemdas is mostly just factoring, kinda. That's how you should think of it.
2x4 is really 2+2+2+2.
That first 2+(anything else) can't be acted/operated upon until you've resolved more nested operations down to a comparable level.
That's it. It's not arbitrary. It's not magic. It's just doing similar actions at the same time in a meaningful way. It's just factoring the activities.
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."
Yeah I haven no idea what I was saying when I said that, I've edited my comment a bit.
On that note though using your example I think I can illistarte the point I was trying to make earlier.
1 + (2*3) by always doing multiplication first we can remove those brackets.
(1 + 2) * 3 can be rewritten as (1 * 3 )+ (2 * 3) so using the first rule again makes a sense. That is a crappy explaination but I think you get my gist.
Your point is not clear.
1 + (2 * 3) by always doing addition first we can remove those brackets.
(1 * 3) + (2 * 3) can be rewritten as (1 + 2) * 3 so using the first rule again makes sense.
Do you see the issue?
I don't see it mate. So you're going to have to tell me, sorry.
The point I'm trying to make is that using Pemdas/Bedmas is the most effiecent way of removing brackets - I actually don't 100% know that but I doubt it creates hundreds of brackets - if thats slightly clearer.
I don't know how else to explain it. I used your own argument verbatim but with the opposite assumption, that addition takes priority over multiplication. In either case, some expressions can be written without parentheses which require parentheses in the other case.
Right well that makes sense. And is also a very good point. I don't really see why you couldn't do that. So I guess it is arbitrary. Although you then have the question of which case occurs more commonly, which is imo actually quite interesting, but also entirely pointless, since good luck showing one case to be more than the other. It's like that door and wheel question.