수학기호의 갯수가 유한한 집합이라고 할 때


수학기호를 쓴다는 것은 그 집합에서 함수를 고르는 행위입니다.


그렇다면 그 수학기호의 정보엔트로피를 구할 수 있을까요?


수학기호는 유한한 집합이 아닐 수도 있는데 이걸 수학적으로 유한하게 만드는 것은 불가능한가요?


참고:


Mathematical Notation: Past and Future-The Future
http://www.stephenwolfram.com/publications/recent/mathml/mathml4.html


"When languages are more or less context free--more or less structured like trees--one can do pretty well with them. Our buffer memory of five chunks, or whatever, seems to do well at allowing us to parse them. Of course, if we have too many subsidiary clauses, even in a context free language, we tend to run out of stack space and get confused. But if the stack doesn't get too deep, we do well."

"Well, I haven't completely solved the problem. But what I've found, at least in many cases, is that there are pictorial or graphical representations that really work much better than any ordinary language-like notation."

"But actually we still don't know a clean simple way to represent things like geometrical diagrams in a kind of language-like notation. And my guess is that actually of all the math-like stuff out there, only a comparatively small fraction can actually be represented well with language-like notation."


http://en.wikipedia.org/wiki/Mathematical_notation

http://en.wikipedia.org/wiki/Penrose_graphical_notation

http://en.wikipedia.org/wiki/Coxeter-Dynkin_diagram


Ambiguously Defined Mathematical Terms at the High School Level
http://jeff560.tripod.com/ambiguities.html


영어가 딸려서 안타깝군요.