wischi

❤️ 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.

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.

Sorry but I don't follow. Did you read the blog post?

Did you read the blog post?

👍 That was actually one of the reasons why I wrote this blog post. I wanted to compile a list of points that show as clear as humanity possible that there is no consensus here, even amongst experts.

That probably won't convince everybody but if that won't probably nothing will.

In a scientific context it's actually very rare to run into that issue because divisions are mostly written as fractions which will completely mitigate the issue.

The strong implicit multiplication will only cause ambiguity after a division with inline notation. Once you use fractions the ambiguity vanishes.

In practice you also rarely see implicit multiplications between numbers but mostly between variables or variables and their coefficients.

Now you changed it to an explicit multiplication. The ambiguity only comes from the implicit multiplication after a division, that's when the interpretation can be ambiguous. That's what the blog post really is about.

If you are not kidding, can you show your steps I can try to help you, but I can't currently think of a way how you'd end up with 15.

❤️