Thread: Minimum Ineffable Behemoth Numerical

Right, absolutely. The reason I went with indexing is because there needs to be some limit placed on the process as I showed in the first paragraph of my first post. Otherwise, the answer to your question is trivially, "No there is no smallest such number." Let's take your example, p(k).

Suppose that you present me with a means of expressing a number with a universe, α; a universe, U; and a number, m, and claim m to be the minimum ineffable number. Then I can just return p.α (. indicates composition) and have a larger representation as we have that p(m) > m.

So you need to specify a particular mapping, in which case the problem becomes boring, or a family of mappings, in which case it may get interesting.