enforce writing math without ambiguity
It already is written without ambiguity.
were taught in third grade
This is actually taught in Year 7 - the people who only remember the 3rd Grade version of the rules are the ones getting it wrong.
SmartmanApps
joined 2 years ago
There isn't ambiguity to begin with - just people who have forgotten the rules of Maths.
I wanted to compile a list of points that show as clear as humanity possible that there is no consensus here, even amongst experts
And I wrote a bunch of fact checks pointing out there is consensus amongst the actual experts - high school Maths teachers and textbook authors, the 2 groups who you completely ignored in your blog post.
What’s especially wild to me is that even the position of “it’s ambiguous” gets almost as much pushback as trying to argue that one of them is universally correct.
That's because following the rules of Maths is universally correct.
arguing vehemently that implicit multiplication having precedence was correct and to do otherwise was wrong, full stop
He was using the wrong words, but he was correct - the actual rules are The Distributive Law and Terms ("implicit multiplication" is a rule made up by those who have forgotten these 2 rules).
Yes, unfortunately there are some bad teachers around. I vividly remember the one I had in Year 10, who literally didn't care if we did well or not. I got sick for an extended period that year, and got a tutor - my Maths improved when I had the tutor (someone who actually helped me to learn the material)!
why that’s actually ambiguous.
It isn't actually ambiguous. You have remembered what you were taught in school, unlike the author of the blog post, who manages to write the whole thing without ever once checking a Maths textbook (which would reveal the only correct answer to be 1).
It treats division like a fraction
Which is why it gives the wrong answer.
Also you shouldn't be adding a dot between the 2 and the brackets - that also changes the answer.
TI calcs give the wrong answer, and it's in their manual why - they only follow the Primary School rule ("inside the brackets"), not the High School rule which supersedes it (The Distributive Law).
It is a funny little bit of notational ambiguity
It's not ambiguous - it's The Distributive Law. You got the correct answer, you just forgot what the rule is called (as opposed to people who forget the rule altogether).
You would've done dividing by fractions in high school, which requires both. Fractions and division aren't the same thing.
But stating the division as a fraction completely changes my mind now about how this calculation works
But division and fraction aren't the same thing - the former separates terms, the latter is a single term.
(140-age)(kg) / 72(SCr) vs (140-age) X kg ➗72 X SCr
The different answers for these two isn't because of / vs ➗, but because in the second one you have added extra multiplications in, thus breaking up some of the terms, and SCr has consequently been flipped from being in the denominator to being in the numerator. i.e. AK/72Scr vs. AK/72xSCr.
You are correct with your definition - Terms are separated by operators and joined by grouping symbols - and it's consequently not ambiguous at all (using so-called "weak juxtaposition" breaks that rule).