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I have a homework problem that says:

For $g(x,y)=xy-5$ compute $h(x) = \mu y(g(x,y))$ and determine its domain.

I was under the impression that this means the least y such that $g(x,y)=0$, so then $y = \frac{5}{x}, D=\{x \in \mathbb{N}, x \neq 0\}$

So $h(x)=\frac{5}{x}$?

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  • $\begingroup$ Is this a computer-science problem? $\endgroup$
    – mrk
    Apr 15, 2013 at 16:17
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    $\begingroup$ I'm studying it as part of a unit on primitive recursion, so ... yes $\endgroup$
    – Stephen
    Apr 15, 2013 at 16:18
  • $\begingroup$ The context has nothing to do with the problem. $\endgroup$
    – mrk
    Apr 15, 2013 at 18:04
  • $\begingroup$ $\mu y.\ \chi(y)$ usually means the least $y$ such that $\chi(y)$ is true. $\endgroup$
    – Pål GD
    Apr 16, 2013 at 6:19

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Hint: $h(x)$ is always a non-negative integer (whenever it's defined).

As a side note, usually primitive recursive functions are assumed to be non-negative, and so $\max(xy-5,0)$ is more usual than what you wrote.

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