I wrote a (very long) blog post about those viral math problems and am looking for feedback, especially from people who are not convinced that the problem is ambiguous.
It’s about a 30min read so thank you in advance if you really take the time to read it, but I think it’s worth it if you joined such discussions in the past, but I’m probably biased because I wrote it :)
Funny how using parentheses gets you the same answer as if implicit multiplication doesn’t have a higher order… It’s almost like considering implicit multiplication as having an advanced order is an invalid assumption to make when looking at a maths equation.
Edit: I’m wrong, read below.
It’s not invalid or even uncommon. It’s just not necessarily correct. Implicit multiplication can be used intentionally to differentiate from explicit multiplication and context can suggest there is a difference in priority. For example, a/bc is likely to be read as a/(bc) because the alternative could be written less ambiguously as ac/b. If I wanted to convey to you that multiplication is associative, I might say ab*c = a*bc, and you’d probably infer that I’m communicating something about the order of operations. But relying on context like this is bad practice, so we always prefer to use parentheses to make it explicit.
It’s only ambiguous if you don’t read left to right. That’s a literacy issue not a mathematics one.
It’s definitely not a mathematics issue. This all concerns only notation, not math. But it’s not a literacy issue either. It’s ambiguous in that the concept of a correct order of operations itself is wrong.
Notation is read left to right, reading it in any other order is automatically incorrect. Just like if you read a sentence out of order you won’t get it’s intention. Like I said, if you actually follow the rules it’s almost like implicit multipication having a higher order doesn’t work, which makes it illigitimate mathematics.
It’s not left to right. a+b*c is unambiguously equal to a+(b*c) and not (a+b)*c.
You determine processing order by order of operations then left to right. Always have. Even in your example, that is the left-most highest order operand, nothing ambiguous about it.
So it’s “higher operands first, then left to right.” I agree. But you presuppose that e.g. multiplication is higher than addition (which, again, I agree with). But now they say implicit multiplication is higher than explicit multiplication. You apparently disagree, but this has nothing to do with “left to right” now.
Just because they say one type of multiplication has precedence doesn’t make it so. We’ve already shown how using parenthesis negates that concept, and matches the output of the method that doesn’t give implicit multiplication precedence, ipso facto, giving ANY multiplication precedence over other multiplication or division doesn’t conform to the rule of highest-operand left to right and doesn’t conform to mathematical notation, and provides an answer that is wrong when the equation is correctly extrapolated with parenthesis, ergo it is utterly conceptually, objectively, and demonstrably, incorrect.
Edit: It was at this moment he realised, he fucked up. Using parenthesis doesn’t resolve to one or the other because the issue is inherent ambiguity in how the the unstated operand is represented by the intention of the writer. They’re both wrong because the writer is leaving an ambiguous assumption in a mathematical notation. Ergo, USE PARENTHESES, ALWAYS.
Correct! “implicit multiplication” is NOT a rule of Maths. It’s something made up by those who don’t remember all the actual rules, which includes The Distributive Law and Terms.