That’s exactly what I did and never looked back. Just installed code-server + a few vs code plugins. Automatically synced via some some scripts that push and pull+merge git commits, done. No need for one of those million note taking apps. I also installed polyglot notebooks for vs code to embed code into notes.
All calculators that are listed in the article as following weak juxtaposition would interpreted it that way.
Regarding your first part in general true, but in this case the sheer amount of calculators for both conventions show that this is indeed intended behavior.
Regarding your second point I tried to address that in the “distributive property” section, maybe I need to rewrite it a bit to be more clear.
@Prunebutt meant 4.5! and not 4.5. Because it’s not an integer we have to use the gamma function, the extension of the factorial function to get the actual mean between 1 and 9 => 4.5! = 52.3428 which looks about right 🤣
Thank you so much for taking the time and reading the post. I just fixed the typos, many thanks for pointing them out.
There is nothing really to be embarrassed about and if you look at the comment sections of such viral math posts you can see that you are certainly not the only one. I think that mnemonics that use “MD” and “AS” without grouping like in “PE(MD)(AS)” are really to blame here.
An alternative would be to drop the inverse and only use say multiplication and addition as I suggested with “PEMA” but with “PEMDAS” one basically sets up students for the problem that they think that multiplication comes before division.
The calculator section is actually pretty important, because it shows how there is no consensus. Sharp is especially interesting with respect to your comment because all scientific Sharp calculators say it’s 1. For all the other brands for hardware calculators there are roughly 50:50 with saying 1 and 9.
So I’m not sure if you are suggesting that thousands of experts and hundreds of engineers at Casio, Texas Instruments, HP and Sharp got it wrong and you got it right?
There really is no agreed upon standard even amongst experts.
I still don’t see a number ;-) but you can take a look at the meme to see other people with math degrees shouting at each other.
The problem with BODMAS is that everybody is taught to remember “BODMAS” instead of “BO-DM-AS” or “BO(DM)(AS)”. If you can’t remember the order of operations by heart you won’t remember that “DM” and “AS” are the same priority, that’s why I suggested dropping “division” and “subtraction” entirely from the mnemonic.
It’s true that calculators also don’t dictate a standard but they implement what conventions are typically used in practice. If a convention would be so dominating (let’s say 95% vs 5%) all calculator manufacturers would just follow the 95% convention, except maybe for some very special-purpose calculators.
Same priority operations are solved from left to right. There is not a single credible calculator that would evaluate “6 / 2 * 3” to anything else but 9.
But I challenge you to show me a calculator that says otherwise. In the blog are about 2 or 3 dozend calculators referenced by name all of them say the same thing. Instead of a calculator you can also name a single expert in the field who would say that 6 / 2 * 3 is anything but 9.
I tried to be careful to not suggest that scientist only use strong juxtaposition. They use both but are typically very careful to not write ambiguous stuff and practically never write implicit multiplications between numbers because they just simplify it.
At this point it’s probably to late to really fix it and the only viable option is to be aware why and how this ambiguous and not write it that way.
As stated in the “even more ambiguous math notations” it’s far from the only ambiguous situation and it’s practically impossible (and not really necessary) to fix.
Scientist and engineers also know the issue and navigate around it. It’s really a non-issue for experts and the problem is only how and what the general population is taught.
Your example with the absolute values is actually linked in the “Even more ambiguous math notations” section.
Geogebra has indeed found a good solution but it only works if you input field supports fractions and a lot of calculators (even CAS like WolframAlpha) don’t support that.
🤣 I’m not sure if you read the post but I also wrote about that (the paragraph right before “What about the real world?”)
In this case it’s actually the absence of sources. I couldn’t find a single credible source that states that ÷ has somehow a different operator priority than / or that :
The only things there are a lot of are social media comments claiming that without any source.
My guess is that this comes from a misunderstanding that the obelus sign is forbidden in a lot of standards. But that’s because it can be confused with other symbols and operations and not because the order of operations is somehow unclear.
That’s the correct answer if you follow one of the conventions. There are actually two conflicting but equally valid conventions. The blog explains the full story but this math problem is really ambiguous.
What is the correct answer according to the convention you follow?
Exactly. With the blog post I try to reach people who already heared that some people say it’s ambiguous but either down understand how, or don’t believe it. I’m not sure if that will work out because people who “already know the only correct answer” probably won’t read a 30min blog post.
I’d really like to know if and how your view on that matter would change once you read the full post. I know it’s very long and a lot of people won’t read it because they “already know” the answer but I’m pretty sure it would shift your perception at least a bit if you find the time to read it.
I’d would be great if you find the time to read the post and let me know afterwards what you think. It actually looks trivial as a problem but the situation really isn’t, that’s why the article is so long.
And now everybody together… C O E V O L U T I O N