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How to prove that this function is primitive recursive?

How should one prove a curve's function?

  • So you know how we have theorems? For example, a questions gives us a statement and demands us to prove the statement right? Similarly, can we do it for curves too? I mean, if a graph of a curve is given and the question demands us to prove that its an exponential/logarithmic/ gaussian/what you may function, can we prove the curve? If yes, then how?

  • Answer:

    Can't be done in general, because the curve is going to be specific by some finite geometric means, while the function may have an infinite domain. Update: Now, about your graph example in comments, as I said below: notice that it ends at x=8 on the right. I know it's obvious how it continues, but for all we know at x=9 the value is 17. So you can't prove that this curve is a sine function.

Hunan Rostomyan at Quora Visit the source

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Given only the graph of a curve, it is impossible to prove what the function of the curve is. Graphs just aren't precise enough. To know for sure what the function is you need to be able to read off exactly what the y value is for every x value, which you obviously can't do (at best, you are limited by the thickness of the line). The best you can do is prove that a particular function is not the right one by showing that there is at least one point where the graph clearly doesn't have the right value. If there are a limited number of functions it could be and you can eliminate all but one of them, then you have proven that it is the remaining function, but that is a very artificial problem. Graphs are a useful tool for getting an intuitive feel for what a function does. You won't find them in the context of rigorous proofs.

Thomas Dalton

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