Post #4366666

@SmartmanApps@dotnet.social Good *grief*, the splaining is strong here. I know what I am talking about here. In particular: "which is unambiguously “six divided by the result of multiplying x by two”" - as is the original expression you wrote No, “six divided by the *result* of multiplying x by two means six divided by *the quantity* 2x.” That’s not the same as “six, divided by two, then *multiplied * by x”. It’s “six, divided by two, then *divided* by x”. "not the same as the ordered sequence" - yes it is No, it is *not*. There is a notational difference here. The expression 6 — 2x *specifically* with a horizontal bar separating the top and bottom expressions, means “divide the result of evaluating the top expression, in its entirety, by the result of evaluating the bottom expression, in its entirety”. It groups the two smaller expressions’ operations *before* doing the division. It has a value of 3/x, which is not the same as the simple term-by-term sequence, which gives 3*x. Yes, really, and if your first response is “no it doesn’t”, then go pull out an elementary algebra text and figure out what 3x-y —— 2+y has to mean. It *always* means “take the quantity 3x-y”, then the quantity “2+y”, then divide them”. It doesn’t insert a division between the “-y” and the “2”, the way that a simple operator sequence like “3x - y ➗ 2 + y” does! This is, in fact, the most common way I’ve seen division represented beyond elementary arithmetic. It is all over the place in literally every mathematics publication I have seen from sometime in middle school through differential equations class in college years ago. And there are reasons for this, like I said, and one of these is precisely to keep a term like “2x” intact in a division, and not have to worry if the “2” becomes a divisor instead of a multiplier because someone forgot a pair of parentheses somewhere. I’m done here. It’s pretty clear you’ve seen lots of elementary arithmetic but don’t seem familiar with topics that are much more advanced than that.