# Have I got the right understanding of the mu operator?

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

• Is this a computer-science problem? – saadtaame Apr 15 '13 at 16:17
• I'm studying it as part of a unit on primitive recursion, so ... yes – Stephen Apr 15 '13 at 16:18
• The context has nothing to do with the problem. – saadtaame Apr 15 '13 at 18:04
• $\mu y.\ \chi(y)$ usually means the least $y$ such that $\chi(y)$ is true. – Pål GD Apr 16 '13 at 6:19

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.