1/a(b+c)=1/(ab+ac)

Nope, that’s wrong. See https://www.wolframalpha.com/input?i=10%2F2(2%2B3) for reference.

I’m a software developer

So am I

adding extra parenthesis often adds clarity

Everyone I’ve seen add Brackets to it has done so in the WRONG place and given WRONG answers. Again this is an issue of programmers not checking the rules of Maths

that do not apply to what I’m talking about

The rules of Maths always apply to all Maths

Take it up with Berkeley then.

Are you under the impression that atomizing your opponents statements and making a comment about each part individually without addressing the actual point (how those facts fit together) is a good debate tactic? Because it seems like all you’ve done is confuse yourself about what I was saying and make arguments that don’t address it. Never mind that some of those micro-rebuttals aren’t even correct.

Please read this section of Wikipedia which talks about these topics better than I could. It shows that there is ambiguity in the order of operations and that for especially niche cases there is not a universally accepted order of operations when dealing with mixed division and multiplication. It addresses everything you’ve mentioned.

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

There is no universal convention for interpreting an expression containing both division denoted by ‘÷’ and multiplication denoted by ‘×’. Proposed conventions include assigning the operations equal precedence and evaluating them from left to right, or equivalently treating division as multiplication by the reciprocal and then evaluating in any order;[10] evaluating all multiplications first followed by divisions from left to right; or eschewing such expressions and instead always disambiguating them by explicit parentheses.[11]

Beyond primary education, the symbol ‘÷’ for division is seldom used, but is replaced by the use of algebraic fractions,[12] typically written vertically with the numerator stacked above the denominator – which makes grouping explicit and unambiguous – but sometimes written inline using the slash or solidus symbol ‘/’.[13]

Multiplication denoted by juxtaposition (also known as implied multiplication) creates a visual unit and is often given higher precedence than most other operations. In academic literature, when inline fractions are combined with implied multiplication without explicit parentheses, the multiplication is conventionally interpreted as having higher precedence than division, so that e.g. 1 / 2n is interpreted to mean 1 / (2 · n) rather than (1 / 2) · n.[2][10][14][15] For instance, the manuscript submission instructions for the Physical Review journals directly state that multiplication has precedence over division,[16] and this is also the convention observed in physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz[c] and mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik.[17] However, some authors recommend against expressions such as a / bc, preferring the explicit use of parenthesis a / (bc).[3]

More complicated cases are more ambiguous. For instance, the notation 1 / 2π(a + b) could plausibly mean either 1 / [2π · (a + b)] or [1 / (2π)] · (a + b).[18] Sometimes interpretation depends on context. The Physical Review submission instructions recommend against expressions of the form a / b / c; more explicit expressions (a / b) / c or a / (b / c) are unambiguous.[16]

6÷2(1+2) is interpreted as 6÷(2×(1+2)) by a fx-82MS (upper), and (6÷2)×(1+2) by a TI-83 Plus calculator (lower), respectively.

This ambiguity has been the subject of Internet memes such as “8 ÷ 2(2 + 2)”, for which there are two conflicting interpretations: 8 ÷ [2 · (2 + 2)] = 1 and (8 ÷ 2) · (2 + 2) = 16.[15][19] Mathematics education researcher Hung-Hsi Wu points out that “one never gets a computation of this type in real life”, and calls such contrived examples “a kind of Gotcha! parlor game designed to trap an unsuspecting person by phrasing it in terms of a set of unreasonably convoluted rules”.[12]

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.

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.

=====

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?

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.

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 am. I’m also telling you.