If that's your idea of reversing the order, then you're not talking about the same thing as SpaceCadet@feddit.nl. They're talking about the order of operations and the associativity/commutativity property. You're talking about the order of the symbols.

I did not flip any signs

Yes you did! 😂

merely reversed the order in which the operations are written out

No, merely reversing the order gives -3-2+1 - you changed the signs on the 1 and 3.

If you read the right side from right to left, it

Starts with -3, which you changed to +3

it has the same meaning as the left side from left to right

when you don't change any of the signs it does 😂

Hell, the convention that the sign is on the left is also just a convention

Nope, it's a rule of Maths, Left Associativity.

Uh, no. I don't think you've thought this through, or you're just using (AS) without realizing it. Conversations around operator precedence can cause real differences in how expressions are evaluated and if you think everyone else is just being pedantic or is confused then you might not underatand it yourself.

Take for example the expression 3-2+1.

With (AS), 3-2+1 = (3-2)+1 = 1+1 = 2. This is what you would expect, since we do generally agree to evaluate addition and subtraction with the same precedence left-to-right.

With SA, the evaluation is the same, and you get the same answer. No issue there for this expression.

But with AS, 3-2+1 = 3-(2+1) = 3-3 = 0. So evaluating addition with higher precedence rather than equal precedence yields a different answer.

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Some other pedantic notes you may find interesting:

There is no "correct answer" to an expression without defining the order of operations on that expression. Addition, subtraction, etc. are mathematical necessities that must work the way they do. But PE(MD)(AS) is something we made up; there is no actual reason why that must be the operator precedence rule we use, and this is what causes issues with communicating about these things. People don't realize that writing mathematical expressions out using operator symbols and applying PE(MD)(AS) to evaluate that expression is a choice, an arbitrary decision we made, rather than something fundamental like most everything else they were taught in math class. See also Reverse Polish Notation.

Your second example, -1+3+2=4, actually opens up an interesting can of worms. Is negation a different operation than subtraction? You can define it that way. Some people do this, with a smaller, slightly higher subtraction sign before a number indicating negation. Formal definitions sometimes do this too, because operators typically have a set number of arguments, so subtraction is a-b and negation is -c. This avoids issues with expressions starting with a negative number being technically invalid for a two-argument definition of subtraction. Alternatively, you can also define -1 as a single symbol that indicates negative one, not as a negation operation followed by a positive one. These distinctions are for the most part pedantic formalities, but without them you could argue that -1+3+2 evaluated with addition having a higher precedence than subtraction is -(1+3+2) = -6. Defining negation as a separate operation with higher precedence than addition or subtraction, or just saying it's subtraction and all subtraction has higher prexedence than addition, or saying that -1 is a single symbol, all instead give you your expected answer of 4. Isn't that interesting?

That’s a very simplistic view of maths

The Distributive Law and Arithmetic is very simple.

It’s convention

Nope, a literal Law. See screenshot

https://en.wikipedia.org/wiki/Order_of_operations

Isn't a Maths textbook, and has many mistakes in it

Just because a definition of an operator contains another operator, does not require that operator to take precedence

Yes it does 😂

2+3x4=2+3+3+3+3=14 by definition of Multiplication

2+3x4=5x4=20 Oops! WRONG ANSWER 😂

As you pointed out, 2+34 could just as well be calculated to 54 and thus 20

No, I pointed out that it can't be calculated like that, you get a wrong answer, and you get a wrong answer because 3x4=3+3+3+3 by definition

There’s no mathematical contradiction there

Just a wrong answer and a right one. If I have 1 2 litre bottle of milk, and 4 3 litre bottles of milk, even young kids know how to count up how many litres I have. Go ahead and ask them what the correct answer is 🙄

Nothing broke

You got a wrong answer when you broke the rules of Maths. Spoiler alert: I don't have 20 litres of milk

You just get a different answer

A provably wrong answer 😂

This is all perfectly in line with how maths work

2+3x4=20 is not in line with how Maths works. 2+3+3+3+3 does not equal 20 😂

add(2, mult(3, 4)), for typical

rule

But it could just as well be mult(add(2, 3), 4), where addition takes precedence

And it gives you a wrong answer 🙄 I still don't have 20 litres of milk

And I hope you see how, in here, everything seems to work just fine

No, I see quite clearly that I have 14 litres of milk, not 20 litres of milk. Even a young kid can count up and tell you that

it just depends on how you rearrange things

Correctly or not

our operators is just convention

The notation is, the rules aren't

Something in between would be requiring parentheses around every operator, to enforce order

No it wouldn't. You know we've only been using brackets in Maths for 300 years, right? Order of operations is much older than that

Such as (2+(3*4))

Which is exactly how they did it before we started using Brackets in Maths 😂 2+3x4=2+3+3+3+3=14, not complicated.