I replied to this effect to someone else in this thread, but I think it's reasonable for people to want to have an idea of what big O is for (in software engineering!) without having to have a grounding in calculus. The notation is useful, and used, without it regularly.
It's reasonable but essentially every "common misconceptions about Big O" is because people didn't have the necessary notions in calculus. For example, the fact that O(x^2) can be practically faster than O(x), due to the size of constants/subdominant terms, is confusing only if you never properly learned what asymptotic behavior is.
The practical question is whether you think it's ok to continue propagating a rather crude and misunderstanding-prone idea about Big O. My stance is that we shouldn't: engineers are not business people or clients, they should understand what's happening not rely on misleading cartoon pictures of what's happening. I do not think you need a full-year collegiate course in calculus to get this understanding, but certainly you cannot get it if you fully obscure the calculus behind the idea (like this and uncountable numbers of blogpost explainers do).
Given the various ways people in this thread have pointed out you lack fluency with the notation, why do you think it reasonable for people to want to learn it without learning the concepts it's describing?
I’m not sure that’s quite my position. Happy to cede that I lack fluency, and I appreciate your time and the time others have given to help me understand.
