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When I was learning statistics I noticed that a lot of things in the textbook I was using were phrased in vague terms of "this is a function of that" e.g. a statistic is a function of a sample from a distribution. I realized that while I know the definition of a function as a relation and I have an intuitive notion of what "function of" means, it's unclear to me how you transform this into a rigorous definition of "function of". So what is the actual definition of "function of"?

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    Very much the same question over at [mathoverflow](https://mathoverflow.net/questions/307947/formalizations-of-the-idea-that-something-is-a-function-of-something-else), posed some years later with other interesting answers.2018-08-21

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