| Popis: |
This paper details an algorithm for a binary, primitive recursive function that apparently computes, for any $i$ and $n$, $f_i\left(i,n\right)$. The algorithm works by exploiting the fact that, in the formal system described, the index assigned to a p.r. function codes the definitional composition of the function. The algorithm exploits such a code to generate a "canonical proof" of $f_i\left(i,n\right)=m$. Since this kind of algorithm is shown impossible by diagonal arguments, the algorithm must be in error. But the error is worth investigating, for it is unclear upon sustained, earnest reflection where it lies. I thus offer this material to readers with a humble request for assistance. |
