Skipping the notation sure is nice and fine as long as you don't end up losing any of its benefits.
The whole idea of notation/language is:
1.to have a common reference for each definition that is explicit
2. forces you to define and handle proofs from a proper angle of detail (think of it like trying to write the specification of a data structure and an algorithm in prose instead of Haskell, C, some assembly dialect. This is actually interesting because what people call "math language" comprises a wide variety of different styles, like programming languages do.
2. concise -- again and again using notation and prior well-defined notions saves a lot of time and space; you don't tangle on the properties of registers for everything you do.
I would say that mathematics has a variety of languages that were, and are introduced per area, to go along. If you have a programming languages background you are familiar with the setting (and joke) that each new work defines a new (somewhat) programming language.
In general, there is a reason computer science is regarded to be that close to math.
The whole idea of notation/language is:
1.to have a common reference for each definition that is explicit 2. forces you to define and handle proofs from a proper angle of detail (think of it like trying to write the specification of a data structure and an algorithm in prose instead of Haskell, C, some assembly dialect. This is actually interesting because what people call "math language" comprises a wide variety of different styles, like programming languages do. 2. concise -- again and again using notation and prior well-defined notions saves a lot of time and space; you don't tangle on the properties of registers for everything you do.
I would say that mathematics has a variety of languages that were, and are introduced per area, to go along. If you have a programming languages background you are familiar with the setting (and joke) that each new work defines a new (somewhat) programming language.
In general, there is a reason computer science is regarded to be that close to math.