error-free notation of arithmetic expressions

For the past two years or so, I’ve been wondering if it’s possible to come up with a language for writing arithmetic expressions that is unambiguous, where each expression would have only one notation, and where every notation would mean something - there wouldn’t be any syntactically incorrect sentences. And yesterday, while discussing this with K., I realized that it’s trivial. Since there are only countably many arithmetic expressions, you just need to sort and number them.

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