Roger Hui <[email protected]> wrote:
> There are probably an uncountable number of such relationships. e.g. 1729
> <https://en.wikipedia.org/wiki/1729_(number)>. Uncountable because there
> are an uncountable number of integer-valued functions on the integers.
Sure. For all n in Z, even the set { f: Z -> Z : f(n) = n } is uncountable,
though it probably makes more sense to limit ourselves to computable functions,
in which case we "just" have a countable collection.
We might get more interesting results by limiting the functions to ones
computable by more restricted computational models like LBA or some such.
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