I mean, it is pretty clear here that you do not really understand the purpose of notation,

says person who doesn't understand that there is only one possible answer to 2+3x4. Even kids who are still counting up know what it is

Notation is just a constructed language to convey a mathematical idea, it’s malleable

Yep, and the rules aren't. 2+3x4 can only ever equal 14. In Germany it's written 2+3.4, and it's still equal to 14, because the rules are universal

Nothing you referenced proved the convention as law

says person ignoring the textbook screenshots explaining why it's a Law 🙄

neither is there any mathematical basis for any proof

Yes there is. See textbook screenshots 🙄

it simply is nonsensical to “prove” a notation

It proves the rules 🙄

Have another source for this being convention https://www.themathdoctors.org/order-of-operations-why/

Read the comments and you'll find multiple people telling him he is wrong, with references 😂 His usual comeback is "well, that doesn't prove that it's taught everywhere", yeah only that they ALL say the same thing! 😂 And he even admitted at one point he couldn't find his rule in any Maths textbooks. 😂 I even tried to tell him myself, and he deleted my comment because I proved he was wrong 😂

or https://math.stackexchange.com/questions/884765/mathematical-proof-for-order-of-operations.

Is well-known to be overridden with people who do not know how to do order of operations 😂 On Mastodon I've seen people asking where is a better place to take Maths problems

If you want a book about this

I have plenty of Maths textbooks, which for some reason you refuse to look in

there’s https://en.wikipedia.org/wiki/Bronshtein_and_Semendyayev that is cited by wikipedia.

"comprehensive handbook" - so, yet again, not a Maths textbook 🙄

"first published in 1945 in Russia" - the order of operations rules are older than 1945 😂

"frequently used guide for scientists, engineers, and technical university students" - notably no mention of Mathematicians

I’m sure you could also find stuff about this in a set theory book

and you could find this in a high school Maths textbook

Though good luck understanding them without sufficient experience in high-level maths

You know teachers here are required to have a Masters in Maths right?? 😂

But why is it the correct answer?

Count up and find out, or use some Cuisenaire rods. This is how young kids learn to do it

In what context?

The context of Addition 🙄

What is the definition of addition?

1+1=2, then inductively proven for all subsequent numbers

How can you prove that 1+1=2 from fundamental axioms?

It's true by definition

This is harder to answer than you might think

Not hard at all. 1+1=2 by definition, then the rest of the numbers are proven inductively. You know there are several species of animals that also know how to count, right?