Of course, there’s also the times where we just make the research hard to do.
Like, we teach kids PEMDAS, but then don’t actually follow PEMDAS in the original textbooks that introduce it and definitely not in common math or physics texts.
Like, you’ll see 1/2√r in Feynman’s lectures being written not to represent ½*√r = √r / 2 as pemdas would suggest, but 1/(2*√r).
Similarly, the original textbooks that introduced PEMDAS, if you read them, actually followed what you might call PEJMDAS, where multiplication via juxtaposition is treated as binding tighter than explicit multiplication, so 1÷2(2+3) would be interpreted not as ½(5) but as 1 ÷ (2 * 5), but they considered that so obvious they didn’t bother to explicitly spell it out in the rules.
And now we have Facebook memes and tiktok livestreams arguing about what 1÷2(2+3) actually means.
Also by the time you’ve learned order of operations, you’ve outgrown the ÷ operator. You would never write 1 ÷ (2 * 5), you would write it with a proper numerator and denominator like anyone outside of elementary school would.
I hate these math problems you see on social media. No one would write that way or code that way. It is ambiguous, and even if it weren’t it is still hard to figure out. I think in my entire career I have seen one single line of code that took PEMDAS to sort out, I remember that line and the programmer told me that they were exploiting a feature of the complier to get slightly faster results. He was an annoying person
Of course, there’s also the times where we just make the research hard to do.
Like, we teach kids PEMDAS, but then don’t actually follow PEMDAS in the original textbooks that introduce it and definitely not in common math or physics texts.
Like, you’ll see 1/2√r in Feynman’s lectures being written not to represent ½*√r = √r / 2 as pemdas would suggest, but 1/(2*√r).
Similarly, the original textbooks that introduced PEMDAS, if you read them, actually followed what you might call PEJMDAS, where multiplication via juxtaposition is treated as binding tighter than explicit multiplication, so 1÷2(2+3) would be interpreted not as ½(5) but as 1 ÷ (2 * 5), but they considered that so obvious they didn’t bother to explicitly spell it out in the rules.
And now we have Facebook memes and tiktok livestreams arguing about what 1÷2(2+3) actually means.
Also by the time you’ve learned order of operations, you’ve outgrown the ÷ operator. You would never write 1 ÷ (2 * 5), you would write it with a proper numerator and denominator like anyone outside of elementary school would.
I hate these math problems you see on social media. No one would write that way or code that way. It is ambiguous, and even if it weren’t it is still hard to figure out. I think in my entire career I have seen one single line of code that took PEMDAS to sort out, I remember that line and the programmer told me that they were exploiting a feature of the complier to get slightly faster results. He was an annoying person
Laughs in RPN
In the UK it’s (or at least was) BODMAS. Just to complicate things further.