Comment on I dunno
FishFace@piefed.social 3 days agoI actually forgot the most obvious way in which Order of Operations is a set of conventions… Some countries say “BODMAS” (division then multiplication) whilst others say “PEMDAS” (multiplication then division)…
mindbleach@sh.itjust.works 3 days ago
They’re grouped, being essentially the same operation, but inverted. Ditto for addition and subtraction. There’s not a convenient word that covers both directions, like how exponents / order are the same for positive and negative powers.
Convention is saying 1/ab is 1/(ab) instead of (1/a)b, while 1/a*b is indeed (1/a)b. The latter of which this troll would say is a syntax error, because juxtaposition after brackets is foreboden… despite modern textbook examples.
FishFace@piefed.social 3 days ago
While reading some of his linked textbooks I found examples which define the solidus as operating on everything in the next term, which would have 1/ab = 1/(ab) = 1/(ab) = 1/ab. This is also how we were taught though as I recall it was not taught systematically: specifically I remember one teacher when I was about 17 complaining that people in her class were writing 1/a·b but should have been writing (1/a)·b (we generally used a dot for multiplication at this point). But at this point in our education, none of us remembered ever being taught this. I suspect what happened was that when being taught order of operations some years before, we simply never used the solidus and only used ÷ or fraction notation.
Anyway, if you have a correct understanding of what the order of operations really are (conventions) you can understand that these conventions all become a bit unwieldy when you have a very complex formula, and that it’s better to write mathematics as if there were no such convention in those cases, and provide brackets for disambiguation. Thus while you might write ab ÷ bc and reasonably expect everyone to understand you mean (ab)/(bc) not ((ab)/b)c (which is what the strict interpretation of PEMDAS would say!) because “bc” just visually creates a single thing, the same is not true of the expression ab ÷ bc(x-1)(y-1)·sin(b), even though bc(x-1)(y-1)·sin(b) is a single term, and so the latter should be written more clearly.
Because DumbMan doesn’t understand mathematical convention, he doesn’t understand that these things really depend on how they’re perceived, so is incapable of understanding such a way of working.
mindbleach@sh.itjust.works 3 days ago
Personally I tend to bracket aggressively, because I’ve been repeatedly betrayed by compilers. One in particular applied the high priority of & (bitwise and) to the low-priority && (logical and), so if( 1 < 2 && 3 ) would always fail because 2 && 3 evaluates to 1.
That was the topic the first time I dealt with this dingus and their rules of maths!!! about a year ago. The post was several months old. They’ve never understood that some things are fundamental… and some things are made up. Some things are mutable. So even if their nonsense was widespread, we could say, that’s kinda stupid, we should do something else.
The dumbest argument I’ve ever suffered online was some dingdong convinced that “two times three” meant the quantity two, three times. Even though “two times” is right there, in the sentence. Even though “twice three” literally means “two times three.” Even though the song “Three Times A Lady” obviously does not mean the quantity three, ladyce. Not even that dipshit thought two times three-squared could be thirty-six.
FishFace@piefed.social 3 days ago
Yeah, I’d make most stuff explicit in programming. You’re rarely gonna do more than two arithmetic operations at a time anyways so you often get it for free. The most common one for me is % which I expect to bind weakly. I guess it binds tightly because it follows division, but I read “a + 1 % n” out loud with a “modulo” and when you say that in a mathematical context the modulo would apply to the entire expression to the left.