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 :)
Notation isn’t semantics. Mathematical proofs are working with the semantics. Nobody doubts that those are unambiguous. But notation can be ambiguous. In this case it is: weak juxtaposition vs strong juxtaposition. Read the damn article.
Read it. Was even worse than I was expecting! Did you not notice that a blog about the alleged ambiguity in order of operations actually disobeyed order of operations in a deliberately ambiguous example? I wrote 5 fact check posts about it starting here - you’re welcome.
Look, this is not the only case where semantics and syntax don’t always map, in the same way e.g.: https://math.stackexchange.com/a/586690
I’m sure it’s possible that all your textbooks agree, but if you e.g. read a paper written by someone who isn’t from North America (or wherever you’re from) it’s possible they use different semantics for a notation that for you seems to have clear meaning.
That’s not a controversial take. You need to accept that human communication isn’t as perfectly unambiguous as mathematics (writing math down using notation is a way of communicating)
Syntax varies, semantics doesn’t. e.g. in some places colon is used for division, in others an obelus, but regardless of which notation you use, the interpretation of division is immutable.
They might use different notation, but the semantics is universal.
Writing Maths notation is a way of using Maths, and has to be interpreted according to the rules of Maths - that’s what they exist for!
No, you can’t prove that some notation is correct and an alternative one isn’t. It’s all just convention.
Maths is pure logic. Notation is communication, which isn’t necessarily super logical. Don’t mix the two up.
I never said any of it wasn’t correct. It’s all correct, just depends on what notation is used in your country as to what’s correct in your country.
No, it’s all defined. In Australia we use the obelus, which by definition is division. In European countries they use colon, which by definition in those countries means division. 1+1=2 by definition. If you wanna say 1+1=2 is just a convention then you don’t understand how Maths works at all.
What you are saying is like saying “there’s no such things as dictionaries, there are no definitions, only conventions”.
Don’t mix up super logical Maths notation with “communication” - it’s all defined (just like words which are used to communicate are defined in a dictionary, except Maths definitions don’t evolve - we can see the same definitions being used more than 100 years ago. See Lennes’ letter).
Yeah, and when you read a paper that contains math, you won’t see a declaration about what country’s notation is used for things that aren’t defined. So it’s entirely possible that you don’t know how some piece of notation is supposed to be interpreted immediately.
Of course if there’s ambiguity like that, only one interpretation is correct and it should be easy to figure out which one, but that’s not guaranteed.
Not hard to work out. It’ll be , for decimal point and : for division, or . for decimal point and ÷ or / for division, and those 2 notations never get mixed with each other, so never any ambiguity about which it is. The question here is using ÷ so there’s no ambiguity about what that means - it’s a division operator (and being an operator, it is separating the terms).
Correct, the definitions and the rules define the semantics.
…the rules of Maths. In fact, when we are first teaching proofs to students we tell them they have to write next to each step which rule of Maths they have used for that step.
Apparently a lot of people do! But yes, unambiguous, and therefore the article is wrong.
Nope. An obelus means divide, and “strong juxtaposition” means it’s a Term, and needs The Distributive Law applied if it has brackets.
There is no such thing as weak juxtaposition. That is another reason that the article is wrong. If there is any juxtaposition then it is strong, as per the rules of Maths. You’re just giving me even more ammunition at this point.
You just gave me yet another reason it’s wrong - it talks about “weak juxtaposition”. Even less likely to ever read it now - it’s just full of things which are wrong.
How about read my damn thread which contains all the definitions and proofs needed to prove that this article is wrong? You’re trying to defend the article… by giving me even more things that are wrong about it. 😂