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		A natural question to ask at this point is whether a similar hierarchy also holds for Bex-identification. The next proposition shows that only a weak analog of Proposition 10.5 for Bex-identification is possible.

		10.7 Proposition For all , .

		Proof: Fix n. We construct a scientist M that Bexn,n-identifies all of . Recall from Chapter 2 that, for each i, s, and x, we define  j i,s(x) =  j i(x), if both x < s and  F i < s; and  j i, s(x) is undefined otherwise. For each j,  s , and x, define:

		Intuitively, S s ,x is a set of programs that appear correct for the given additional information x and the finite initial segment  s . For each j and  s , let patch( s , j) be a program that computes

		Thus, if j is a program that computes f with at most n errors, then, for sufficiently large s, program patch(f[s], j) will not make any convergent errors. For each finite set A, let Unify(A) be a program that computes

		Clearly, we can take errors, patch, and Unify to be recursive. Finally, for each  s  and x, we define

		Fix an and an . Then for sufficiently large s, the only errors program makes are divergent errors whose total count is bounded by n. Therefore, M Bexn,n-identifies f as required.

		Let us contrast the result above with the following proposition which shows that the n = * analog of Proposition 10.7 fails.

		10.8 Proposition .