 If \(A\) is c.e., then it is clear that \(A\) is limit computable. For if \(A\) is the range of a computable function \(\phi_e(x)\), then we may take \(A^s\) to be \(\{\phi_e(0), \ldots, \phi_e(s)\}\) in which case \(A^0 \subseteq A^1 \subseteq A^2 \subseteq \ldots\) In the general case of limit computability, the sequence of sets \(\{A^s : s \in \mathbb{N}\}\) may be thought of as an approximation of \(A\) which need not grow monotonically in this way but can rather both grow and shrink as long as there is always a stage \(s\) such that for all \(s \leq t\), \(n \in A^t\) if \(n \in A\) and \(n \not\in A^t\) if \(n \not\in A\). Following Putnam (1965), a limit computable set can also thus also be described as a so-called trial-and-error predicate—i.e., one for which membership can be determined by following a guessing procedure which eventually converges to the correct answer to the questions of the form \(n \in A\)?