I have developed the next conjecture:
CONJECTURE: The set of all partial functions in $\mathbb{N}$, $f:(0,n)\rightarrow (0,n)$, being n a finite natural number, is a set of computable functions, and the cardinality of this set is $n^n$ (finite).
I think that there are no NON-computable functions in $\mathbb{N}$, $f:(0,n)\rightarrow (0,n)$, because this set is finite. Could you please tell me if this is correct?