Abstract

We define a function γ:N→N which eventually dominates every computable function α:N→N. We show that there is a computer program which for n∈N prints the sequence {γ_i(n)}_{i=0}^∞ of non-negative integers converging to γ(n). We define a function β:N→N of unknown computability which eventually dominates every function δ:N→N with a single-fold Diophantine representation. We show that there is a computer program which for n∈N prints the sequence {β_i(n)}_{i=0}^∞ of non-negative integers converging to β(n). Let Γ denote the following statement: ∃f:N→N of unknown computability such that f eventually dominates every function δ:N→N with a single-fold Diophantine representation and there is a computer program which for n∈N prints the sequence {f_i(n)}_{i=0}^∞ of non-negative integers converging to f(n). We show that Γ has all properties from the title of the article.