Convention of order of operations

[Mr Davis 97]

To what extent is the PEMDAS order of operations convention, and to what extent is this convention significant? For example, how would math change if we stipulated that $1+2*3 = 3*3 = 9$? Would it be the same or would it be completely different?

 

[John Park]

You'd have to write things differently; e.g. 1 + (2*3) = 1 + 6 = 7. I tend to think the present convention is convenient but I could well be biased. I can't see any fundamental changes happening if we switched to a different convention: important changes would only occur if some expressions became impossible or very awkward to write--or suddenly much easier--and I can't think of any that would be.

Of course, if we did switch, it would be like suddenly having to drive on the other side of the road and reading mathematics written before the change would be like reading a foreign language.

 

[fresh_42]

To what extent is the PEMDAS order of operations convention, and to what extent is this convention significant? For example, how would math change if we stipulated that $1+2*3 = 3*3 = 9$? Would it be the same or would it be completely different?

If you want to have a look what happened last time we discussed this ...
https://www.physicsforums.com/threads/biggest-science-or-math-pet-peeve.885541/
(I don't remember where exactly in this thread PEDMAS started, but once it did, you barely couldn't get rid of it.)

 

[Svein]

Change to reverse Polish notation!

((1+2)*3 ⇒ 1⊥2+3*, 1 + (2*3) ⇒1⊥2⊥3*+) (the ⊥ sign is just used to indicate "enter")

 

[John Park]

Cute. (But several decades after it was introduced on calculators, RPN doesn't seem to have really caught on for some reason.)