Supporting the improvement and refinement of existing ways of thinking and knowledge systems in terms of their own needs. For example, only letters are used to represent unknowns in generally considered algebraic equations:
Identifier naming in mathematical algorithms from a code readability perspective
The truth is that everyone can construct a body of knowledge that works for them, even in math.
What is ‘basic’ and what is ‘upper’ is not necessarily one-size-fits-all.
Across the board, even one person can have multiple perspectives.
What is important is the process of knowledge reconstruction, and one effective way to do this is to ‘tell it again in your own words’.
The operators of calculus in those days were expressed in several ways by various authors:
It is now possible to try to express the same semantics in your own design when you first learn the various points of mathematics, comparing strengths and weaknesses and revising your understanding in the process.
It’s normal for things to be more or less the same in the beginning, but gradually there will always be a little bit of revision and breakthrough here and there, just as computer languages are still evolving after more than seventy years of development.