Order of Operations?

So, where did the order of operations come from and how is it justified? So many times do I see pictures like this on the interwebs and people debate over it. Why is it that we do operations in the order that we do?

answer is 5 btw

Convention

The only use I have ever encountered in my life was with programming languages, but for all intents and purposes it is as arbitrary as psychology.

Math allows people to write shit ambiguously.

Arguments come from unclear statements, like 3+4/3+2

Which can arguable read as
(3+4)/(3+2)
or
3+(4/3)+2
or
((3+4)/3)+2
and etc

that's the stupidest thing I've ever read

Because exponentiation is just a short hand notation for a bunch of multiplications. And multiplications are a shorthand notation for a bunch of additions. Parenthesis are just an artificial way of grouping operations in the way the author wants them to.

So if you have an exponentiation and a multiplication you need to do the exponentiation first since it's just a shorthand, and you can't do a multiplication between a number and a shorthand notation, since it doesn't make any sense. The same goes for multiplication and addition, since multiplication is just a shorthand.

Practically all arithmetic operations are nothing more than additions, with shorthand notation used to not have to write millions of repeating numbers.

Tell me about the great mathematical field of order of operations oh wise one.

Is it really as arbitrary as convention? No logic behind it at all?

>Veeky Forums read left to right
>/math/ just fuck my shit up

It is logic + convention.

Logic because you have to choose an order that was consistent (if you follow its rules then you must always get an unique answer) but there are many possible ways to make it consistent and picking one is indeed arbitrary convention.

That was such an autistic way to say it was arbitrary. Impressed user.

You also read left to right 8-5-3=0

The answer is negative five hundo

except for exponents

3^3^3 = 3^27 not (3^3)^3=3^9

It is convention. It has logic behind it. They are not mutually exclusive.

The distributive law in a ring says a(b+c) = ab + ac. You can deduce the "order of operations" (what a fucking brainlet middle schooler term give me a fucking break) from that

There's nothing unclear about that statement.

is this bait? it honestly made me mad at how someone could be such an imbicile but then again how would they be able to use a computer.

>/a/ right to left
>/pol/ don't read at all
>/x/ everything you read is brainwashing propaganda

What?

The order was established so that we get the correct answer.