What is this "order of operation" cult now with math?

[Vtile]

(04-05-2021 11:03 PM)toml_12953 Wrote:  

(04-05-2021 09:39 AM)Vtile Wrote:  For me it seems that this confusion or split have become true when people started to interface with computers (parsing classic paper infix notation with hidden brackets and many times 2-dimensions for computer 1-dimensional entry) and then with bedacocy justification some group got the idea that pupils should be prepared for computers, because computers are scary and stupid. Soup was set.

Now it seems that there is loosely a two and half groups.
The ones that read one line expressions like computer (but adding hidden symbols, which compilers do not do)
The ones that read one line expression like it was a print paper.
The last half that try to deduct the right aproach from content or say directly that something is ambiqyous. (Most math. uni. Profs seems to be on this group, which is wise I must admit[/b].)

We were always taught that implied multiplication is still multiplication so it's treated the same as if the multiplication symbol is in there and is at the same priority level as division.

I think I have thought something similar at least the hierarchy is the same as in most countries, but the only difference seems to be this implied multiplication and how it groups things together and I don't think that any teacher is pushed it at all, it just have been naturally formed .. maybe?

If I do see one line expression like:
\begin{equation}
1(3-1)/2(1+1)
\end{equation}

..the expression I do actually instantly internalize and see is:
\begin{equation}
\frac{1(3-1)}{2(1+1)}
\end{equation}

Nothing like this:
\begin{equation}
\frac{1(3-1)}{2}\times (1+1)
\end{equation}

Or not even this:
\begin{equation}
\frac{1(3-1)(1+1)}{2}
\end{equation}

...And definitely not:
\begin{equation}
EVAL(3-1)
\end{equation}

Unfortunately this doesn't have enough daylight that there actually is more than one way to analyse these. For me now that I have studied a bit on the subject I'm more aware of this and will use for the future the ambiguous card, since both have their merits, while I do personally lean the side of implied multiplication grouping (...for human consumed expressions, compilers have manuals).