[simion314]

Can you just give me an example? Like link to your work or someone else(preferably a mathematician) that does rigorous proofs using natural language. Maybe i do not understand exactly your point, you want some symbols so what is the rule what symbols are allowed and what not.

Not sure what you mean about defining a set, as I mentioned in Math fundamentals you have no choice then to define a few initial primary terms and axioms to bootstrap things.