I’m not sure if I’d call it the “scientific” one. I’d actually say that the weak juxtaposition is just the simple one schools use because they don’t want to confuse everyone. Scientist actually use both and make sure to prevent ambiguity. IMHO the main takeaway is that there is no consensus and one has to be careful to not write ambiguous expressions.
It’s not really a calculator engineering problem. If you don’t have time to read the entire blog you should definitely check out the section “But my calculator says…”. It’s actually about order of operations regarding implicit multiplication.
Thank you so much for taking the time. I’m also not convinced that APS’s notation is a very good choice but I’m neither american nor a physisist 🤣
I’d love to see how the exceptions work that the APS added, like allowing explicit multiplications on line-breaks, if they still would do the multiplication first, but I couldn’t find a single instance where somebody following the APS notation had line-break inside an expression.
❤️ True, but I think one of the biggest problems is that it’s pretty long and because you can’t really sense how good/bad/convining the text is it’s always a gamble for everybody if it’s worth reading something for 30min just to find out that the content is garbage.
I hope I did a decent job in explaining the issue(s) but I’m definitely not mad if someone decides that they are not going to read the post and still comment about it.
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.
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.
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.
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.
The full story is actually more nuanced than most people think, but the post is actually very long (about 30min) so thank you in advance if you really find the time to read it.
@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 🤣