The underlying truth of this joke is: Programming syntax is less confusing than mathematical syntax. There are genuinely ambiguous layouts of syntax in math (to a human reader that hasn't internalized PEMDAS, anyways) whereas you get a compilation error if ANYTHING is ambiguous in programming. (yes, I am WELL aware of the frustrations of runtime errors)
But when I learned BEDMAS, my teacher directed us to do implied multiplication before other multiplication/division. Which, as far as I'm aware, is mathematically correct according to the proper order of operations (instead of whatever acronym summary you learned).
Before I get "umm. Acktually"d .... I know that's not the full picture of the order of operations as it should be in mathematics. But for the limited scope I learned of algebra from highschool, AFAIK, this is correct to the point that I have understanding of. I'm not a mathematician, and I work with computers all day long and they do the math for me when I need to do any of it. So higher understanding in my case is not helpful.
AFAIK, this is correct to the point that I have understanding of. I’m not a mathematician
I'm a Maths teacher/tutor. The actual rules are Terms and The Distributive Law. There is no such thing as "implicit multiplication" (which is usually people lumping the 2 separate rules together as one and ending up with wrong answers).
Order is often used to describe exponents when talking about functions and other mathematical properties. In a lot of cases, it's also equivalent to a degree. For example, a function y = x² - 9 is a second-order/degree polynomial.
Alternatively, one could find a second-order rate of a reaction, which means the rate of reaction is proportional to the square of a solution's concentration.
You have the right idea, and you are right in some regards. Generally the order of magnitude is an order of 10. That is, 1350 could be represented as 1.350×10³, so the order of magnitude is the third order of 10, which is 10³ (i.e. some value x×1000).
Every single Maths textbook I've seen teaches it correctly. The issue is people not remembering what they were taught (and then programming a calculator without checking it first). Calculators
Also: sometimes, a mathematician just has to invent some concept or syntax to convey something unconventional. The specific use of subscript/superscript, whatever 'phi' is being used for, etc. on whatever paper you're reading doesn't have to correlate to how other work uses the same concepts. It's bad form, but sometimes its needed, and if useful enough is added to the general canon of what we call "math". Meanwhile, you can encapsulate and obfuscate things in software, sure, but you can always get down to the bedrock of what the language supports; there's no inventing anything new.
Yea, that's it. Math syntax was created for humans, and programming syntax had to always remain deterministic for computers. It's not an insult to either, just interesting how ambiguities show up often when humans are involved. I say 'often' for the general case: Math should be just as deterministic as programming, but it's not in some situations.