How to prove rigorously that Conway's chained arrow notation defines a unique function?
问题内容
I know of Conway's chained arrow notation. I have read the Wikipedia article on it, but it still didn't give me a rigorous proof that it exists and is unique. So, to make my question precise, suppose we are given a finite nonempty sequence $S$ of positive integers. How does one rigorously define the Conway chained arrow function $C(S)$? And also, given the recursive definition, how does one prove that it actually defines a unique function?
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