I think it was something like : -2 is a diminutive for -1x2

Correct. Things that are usually left out of Maths expressions are plus signs, ones as multipliers/indices, and un-needed brackets. e.g. I could more fully write this as -1(4)², but that just simplifies to -4²

Yeah, didn't think that came from any textbook.

And also if I hadn't been replying to this thread then you wouldn't have got the proof that you were right. :-)

Except TI calculators also give the wrong answer when a bracketed term has a coefficient.

There's no multiplication in this question - multiplication refers literally to multiplication signs - only division and brackets, and addition within the brackets. So you have to use The Distributive Law to solve the brackets, then do the division, giving you 1.

2-(2-2)

But you broke the rule of left-associativity there. You can go right to left provided you keep each number with the sign to it's left (and you didn't do that when you separated the first 2 in brackets from it's minus sign).

I’ve never had anyone tell me operations with the same priority can be done either way, it’s always been left to right

It's left to right within each operator. You can do multiplication first and division next, or the other way around, as long as you do each operator left to right. Having said that, you also can do the whole group of equal precedence operators left to right - because you're still preserving left to right for each of the two operators - so you can do multiplication and division left to right at the same time, because they have equal precedence.

Having said that, it's an actual rule for division, but optional for the rest. The actual rule is you have to preserve left-associativity - i.e. a number is associated with the sign to the left of it - and going left to right is an easy way to do that.

Are you for real?

Yes, I'm a Maths teacher.

A fraction is a shorthand for division with stronger (and therefore less ambiguous) order of operations

I added emphasis to where you nearly had it.

½ is a single term. 1÷2 is 2 terms. Terms are separated by operators (division in this case) and joined by grouping symbols (fraction bars, brackets).

1÷½=2

1÷1÷2=½ (must be done left to right)

Thus 1÷2 and ½ aren't the same thing (they are equal in simple cases, but not the same thing), but ½ and (1÷2) are the same thing.

It’s not a law of maths in the way that 1+1=2 is a law

Yes it is, literally! The Distributive Law, and Terms. Also 1+1=2 isn't a Law, but a definition.

So 1/2x is universally interpreted as 1/(2x)

Correct, Terms - ab=(axb).

people doing academic research in maths, not primary school teachers

Don't ask either - this is actually taught in Year 7.

if they realise it’s over a question like this they’ll probably end up saying “it’s deliberately ambiguous in an attempt to start arguments”

The university people, who've forgotten the rules of Maths, certainly say that, but I doubt Primary School teachers would say that - they teach the first stage of order of operations, without coefficients, then high school teachers teach how to do brackets with coefficients (The Distributive Law).

infix doesn’t have any ambiguity either if you parenthesize all operations like that

There isn't any ambiguity even if you don't.

Ditto for Sharp. It's really only Texas Instruments that is the ongoing exception to the rule.

Pays to know how to recover code from the reflog in these cases.

At first I read that as re-flog. Is that with a cat o' nine tails? 😂