I think I learned powers take priority over the “-”
Yes, Exponents is the 2nd-highest precedence (after Brackets) - BEDMAS.
Division and multiplication are equal in the order of operations
I didn't say they weren't. I said...
Doing division before brackets goes against the order of operations rules
You did 8/2x4, which is the same as (8/2)(2+2), which isn't the same as 8/2(2+2)=8/2(4)=8/(2x4).
let me take this seriously for a second
You need to take it seriously for longer than that.
implies that they are provably distinct functions
No, I'm explicitly stating they are.
we can use the usual set-theoretic definition
This is literally Year 7 Maths - I don't know why some people want to resort to set theory.
Can you give me such a pair of numbers?
But that's the problem with your example - you only tried it with 2 numbers. Now throw in another division, like in that other Year 7 topic, dividing by fractions.
1÷1÷2=½ (must be done left to right)
1÷½=2
In other words 1÷½=1÷(1÷2) but not 1÷1÷2. i.e. ½=(1÷2) not 1÷2. Terms are separated by operators (division in this case) and joined by grouping symbols (brackets, fraction bar), and you can't remove brackets unless there is only 1 term left inside, so if you have (1÷2), you can't remove the brackets yet if there's still some of the expression it's in left to be solved (or if it's the last set of brackets left to be solved, then you could change it to ½, because ½=(1÷2)).
Therefore, as I said, division and fractions aren't the same thing.
apologise for the smugness
Apology accepted.
neither defines wether implied multiplication is a multiply/divide operation or a bracketed operation
The Distributive Law says it's a bracketed operation. To be precise "expand and simplify". i.e. a(b+c)=(ab+ac).
1/2x and expect you to know which one I meant with no additional context or brackets
By the definition of Terms, ab=(axb), so you most certainly can write that (and Maths textbooks do write that).
It's not taught 2 different ways. It's taught the same around the world (the mnemonics are different but the rules are the same), there's just 2 types of people - those who remember the rules and those who don't. You'll notice students never get these questions wrong, only adults who've forgotten the rules.
you’re a slow reader
I see you like to use made-up "facts", just like the blog does. Is that the best you can come up with after repeatedly insisting I should read it? (which yes, would've been a huge waste of time, exactly as I said, had I not turned it into a positive use of time by writing a fact check about it. Alleged fake news turns out to be... fake - who would've thought? Oh that's right, me :-) )
I’ll read your comment when you read the article
So, did you read it now? Or are you a "slow reader" and I need to wait longer for your responses?
I've narrowed this down to using NavigationPage.SetTitleView and have created issue 21037, which has an 806issue branch in the repro repo.
The ÷ sign isn’t used by “Americans”, it’s used by small children
I don't know where you're from, but it's used universally in Australia - textbooks, calculators, all ages - and from what I've seen the U.K. too.
written like this (÷) means it’s a fraction?
No, that means it's a division. i.e. a÷b. To indicate it's a fraction it would need to be written as (a÷b). i.e. make it a single term. Terms are separated by operators and joined by grouping symbols (such as brackets or fraction bars).
put the whole 2(1+2) down there, there’s no reason for that.
There is - it's a single bracketed term, subject to The Distributive Law. i.e. the B in BEDMAS.
And if you don't then you can no longer claim they are still equal.