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 :)
There has apparently been historical disagreement over whether 6÷2(3) is equivalent to 6÷2x3
As a logician instead of a mathemetician, the answer is "they're both wrong because they have proven themselves ambiguous". Of course, my answer would be RPN to be a jerk or just have more parens to be a programmer
No, there hasn't - that's a false claim by a Youtuber (and others who repeated it) - it is equal to 6÷(2x3) as per The Distributive Law and Terms, and even as per the letter he quoted! Here is where I debunked that claim.
Are you referring to Presh Talwalkar or someone else? How about his reference for historical use, Elizabeth Brown Davis? He also references a Slate article by Tara Haelle. I've heard Presh respond to people in the past over questions like this, and I'd love to hear his take on such a debunking. I have a lot of respect for him.
Your "debunk" link seems to debunk a clear rule-change in 1917. I wouldn't disagree with that. I've never heard the variant where there was a clear change in 1917. Instead, it seems there was historical vagueness until the rules we now accept were slowly consolidated. Which actually makes sense.
The Distributive Law obviously applies, but I'm seeing references that would still assert that (6÷2) could at one time have been the portion multiplied with the (3).
And again, from logic I come from a place of avoiding ambiguity. When there is a controversiallly ambiguous form and an undeniablely unambiguous form, the undeniably unambiguous form is preferable.
Yes, the guy who should mind his own business.
Are you talking about his reference to Lennes' letter? Lennes' letter actually completely contradicts his claim that it ever meant anything different.
Haven't seen that one. Do you have a link?
...a journalist. The article ALSO ignores The Distributive Law and Terms.
Thank you. And also thank you for being the first person to engage in a proper conversation about it here.
I've seen him respond to people who agree with him. People who tell him he's wrong he usually ignores. When he DOES respond to them he simply says "The Distributive Property doesn't apply". We're talking about The Distributive LAW, NOT the Distributive Property. It's called "law" for a reason. i.e. ALWAYS applies. I've only ever seen him completely unwilling to engage in any conversation with anyone who points out he's wrong (contradicting his claim that he "welcomes debate").
Really?? Why's that? I'm genuinely curious.
Me either. As far as I can tell it's just people parroting his misinterpretation of Lennes' letter.
I can't agree with that. Lennes' letter shows the same rules in 1917 as we use now. Cajori says the order of operations rules are at least 400 years old, and I have no reason to suspect they changed at all during that time period either. They're all a natural consequence of the way we have defined the symbols in the first place.
Again, thank you.
If it was written (6÷2)(1+2), absolutely that is the correct thing to do (expanding brackets), but not if it's written 6÷2(1+2). If you mean the latter then I've never seen that - links?