> So, until you are able to perform this "translation" from precise to imprecise notation, I suggest you stick to the precise notation, until all the fundamenta

> So, until you are able to perform this "translation" from precise to imprecise notation, I suggest you stick to the precise notation, until all the fundamental concepts are clear, and only then abuse notation. I agree with this part. I think in teaching, the precise notation should be taught first and everyone should understand it well. But later on, it will make communication and even just doing calculations easier if you can accept the imprecise notation, use it and translate it into something clearer when needed. This is particularly handy in e.g. differential equations where sloppy notation makes certain manipulations a bit easier.