I cannot stress this enough. If you have a problem with that, contact the author or Berkeley, not me
I cannot stress this enough - look in Maths textbooks, not random University blogs 😂
Just patently untrue,
Maths textbooks are patently untrue?? 😂 I guess you think Earth is flat too
Take it up with Berkeley then
What for? You're only the second person ever to have quoted him. You're not the first person to refuse to look in Maths textbooks though 🙄
this is just a writing standard that is globally agreed on
No, it's a universal rule of Maths
The writing rules are defined by humans not by natural force
Maths is for describing natural forces, and is subject to those laws
That one thing and another thing are two things, is a rule from nature
Yep, there are even some animals who understand that, and all of Maths is based upon it.
That’s not even an equation, just basic arithmetic
Basic Algebra actually. Students aren't taught the Distributive Law until they start on Algebra
insist mathematics has exactly one perfect unambiguous syntax,
It sure does! 😂
2*(1+3) is somehow different from 2(1+3)
Yep, one is Multiplication - 2x3 - the other is The Distributive Law - (2x1+2x3) - both easily found in Maths textbooks
because there is no context given
None needed. Obey the rules of Maths and you get the correct answer.
the order of operations or what those operations are exactly would be clear through the context of these formulas
It's clear to anyone who knows the rules of Maths.
Thanks for the effort!
You're welcome.
You can define your notation that way if you like
Nothing to do with me - it's in Maths textbooks.
without knowing the conventions the author uses, it’s ambiguous
Well they should all be following the rules of Maths, without needing to have that stated.
Your argument is circular in nature
No it isn't. The order of operations rules are derived from the definitions of the operators - there's nothing circular about that.
The right answer is dependent upon the order that you do the operations
And so to get the correct answer, you have to do the operations in the correct order, yes.
So you can’t use the argument that the order of operation matters
But you just said it did when you said "The right answer is dependent upon the order that you do the operations"!
if you do the math not using the correct order of operations, the answer comes out incorrectly
Exactly! Glad you agree with me. :-)
we could just do away with order of operations all together and explicitly use parentheses everywhere
Except I showed here that most people put brackets in the wrong place to begin with.
So there’s nothing inherently correct about our current order of operations
I already gave the proof of why it is. We already know that 2x3=2+2+2 by definition, so therefore 2+2x3=2+6=8. If you did addition first you'd get 2+2x3=4x3=12, which is demonstrably wrong. Welcome to how the order of operations rules were derived to begin with.
I will say that I like it and that it makes sense to me
It makes sense because it's been proven to be correct.
It isn’t, because the ‘currently taught rules’ are on a case-by-case basis and each teacher defines this area themselves
Nope. Teachers can decide how they teach. They cannot decide what they teach. The have to teach whatever is in the curriculum for their region.
Strong juxtaposition isn’t already taught, and neither is weak juxtaposition
That's because neither of those is a rule of Maths. The Distributive Law and Terms are, and they are already taught (they are both forms of what you call "strong juxtaposition", but note that they are 2 different rules, so you can't cover them both with a single rule like "strong juxtaposition". That's where the people who say "implicit multiplication" are going astray - trying to cover 2 rules with one).
See this part of my comment... Weak juxtaposition provides better benefits because it has less rules (and is thusly simpler)
Yep, saw it, and weak juxtaposition would break the existing rules of Maths, such as The Distributive Law and Terms. (Re)learn the existing rules, that is the point of the argument.
citation needed
Well that part's easy - I guess you missed the other links I posted. Order of operations thread index Text book references, proofs, the works.
this issue isn’t a mathematical one, but a grammatical one
Maths isn't a language. It's a group of notation and rules. It has syntax, not grammar. The equation in question has used all the correct notation, and so when solving it you have to follow all the relevant rules.
And there's no such thing as either 🙄