6÷2(1+2)
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 :)
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I disagree. Without explicit direction on OOO we have to follow the operators in order.
The parentheses go first. 1+2=3
Then we have 6 ÷2 ×3
Without parentheses around (2×3) we can't do that first. So OOO would be left to right. 9.
In other words, as an engineer with half a PhD, I don't buy strong juxtaposition. That sounds more like laziness than math.
How are people upvoting you for refusing to read the article?
Because those people also didn't read the article and are reacting from their gut.
are reacting from their gut
As was the person who wrote the article. Did you not notice the complete lack of Maths textbooks in it?
I did read the article. I am commenting that I have never encountered strong juxtaposition and sharing why I think it is a poor choice.
You probably missed the part where the article talks about university level math, and that strong juxtaposition is common there.
I also think that many conventions are bad, but once they exist, their badness doesn't make them stop being used and relied on by a lot of people.
I don't have any skin in the game as I never ran into ambiguity. My university professors simply always used fractions, therefore completely getting rid of any possible ambiguity.
You probably missed the part where the article talks about university level math,
This is high school level Maths. It's not taught at university.
I have never encountered strong juxtaposition
There's "strong juxtaposition" in both Terms and The Distributive Law - you've never encountered either of those?
Because as a high school Maths teacher as soon as I saw the assertion that it was ambiguous I knew the article was wrong. From there I scanned to see if there were any Maths textbooks at any point, and there wasn't. Just another wrong article.
Lol. Read it.
Why would I read something that I know is wrong? #MathsIsNeverAmbiguous
Mathematical notation however can be. Because it's conventions as long as it's not defined on the same page.
Mathematical notation however can be.
Nope. Different regions use different symbols, but within those regions everyone knows what each symbol is, and none of those symbols are in this question anyway.
Because it’s conventions as long as it’s not defined on the same page
The rules can be found in any high school Maths textbook.
Let's do a little plausibility analysis, shall we? First, we have humans, you know, famously unable to agree on an universal standard for anything. Then we have me, who has written a PhD thesis for which he has read quite some papers about math and computational biology. Then we have an article that talks about the topic at hand, but that you for some unscientific and completely ridiculous reason refuse to read.
Let me just tell you one last time: you're wrong, you should know that it's possible that you're wrong, and not reading a thing because it could convince you is peak ignorance.
I'm done here, have a good one, and try not to ruin your students too hard.
unable to agree on an universal standard for anything
And yet the order of operations rules have been agreed upon for at least 100 years, possibly at least 400 years.
unscientific and completely ridiculous reason refuse to read
The fact that I saw it was wrong in the first paragraph is a ridiculous reason to not read the rest?
Let me just tell you one last time: you’re wrong
And let me point out again you have yet to give a single reason for that statement, never mind any actual evidence.
you should know that it’s possible that you’re wrong
You know proofs, by definition, can't be wrong, right? There are proofs in my thread, unless you have some unscientific and completely ridiculous reason to refuse to read - to quote something I recently heard someone say.
try not to ruin your students too hard
My students? Oh, they're doing good. Thanks for asking! :-) BTW the test included order of operations.
Just read the article. You can't prove something with incomplete evidence. And the article has evidence that both conventions are in use.
You can’t prove something with incomplete evidence
If something is disproven, it's disproven - no need for any further evidence.
BTW did you read my thread? If you had you would know what the rules are which are being broken.
the article has evidence that both conventions are in use
I'm fully aware that some people obey the rules of Maths (they're actual documented rules, not "conventions"), and some people don't - I don't need to read the article to find that out.
as an engineer with half a PhD
As an engineer with a full PhD. I'd say we engineers aren't that great with math problems like this. Thus any responsible engineer would write it in a way that cannot be misinterpreted. Because misinterpreted mathematics can kill people...
The oxford comma approach, I agree.
As an engineer with a full PhD. I’d say we engineers aren’t that great with math problems like this
Yay for a voice of reason! I've yet to see anyone who says they have a Ph.D. get this correct (I'm a high school Maths teacher/tutor - I actually teach this topic).
Yeah, but implicit multiplication without a sign is often treated with higher priority.
Sure. That doesn't mean it's right to do.
Please read the article, that's exactly what it's about. There is no right answer.
Let them fight.
There is a right answer. Read this instead dotnet.social/@SmartmanApps/110897908266416158
I read the article, and it explained the situation and the resultant confusion very well. That said, could we not have some international body just make a decision one way or the other, instead of perpetuating this uncertainty?
It's practically impossible to do that because (applied) mathematics is such a diverse field and there is no global authority (and really can't be).
Math notation is very similar to natural languages what you are proposing is a bit like saying we have an ambiguity in english with the word "bat". It can mean the animal or the sport device. To prevent confusion the oxford dictionary editors just decide that from now on "bat" only refers to the animal and not the club. Problem solved globally? Probably not :-)
What you can do/try is to enforce some rules in smaller groups, like various style guides and standards are trying to do. For example it's way simpler for a university to enforce certain conventions and styles for the work they and their students produce. But all engineers in Belgium couldn't care less what a university in India is thinking about math notations.
For real projects that involve many people there are typically industry standards that are followed that work a bit like in the university example and is enforced by the participants of the project.
could we not have some international body just make a decision one way or the other
There's no decision to be made. The correct rules are already taught in literally every Year 7-8 Maths textbook.
Is it though? I've only ever seen it treated as standard multiplication.
Read TFA
as a half PhD
Go read the article, it's about you
Go read the article, it’s about you
The article is wrong dotnet.social/@SmartmanApps/110897908266416158
Without parentheses around (2×3)
But there is parentheses around (2x3). a(b+c)=(ab+ac) - The Distributive Law. You can't remove them unless there is only 1 term left inside. You removed them when you still had 2 terms inside, 2x3.
6/2(1+2)=6/2(3)=6/(2*3)=6/6=1
OR
6/2(1+2)=6/(2+4)=6/6=1