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		infinite string of #'s; alternatively (if the language is nonempty), it must present at least one sentence infinitely often.

		The foregoing picture of the child's linguistic environment is motivated by studies of language acquisition. Several investigations (for example, Brown and Hanlon [22], Hirsh-Pasek, Treiman, and Schneiderman [81], and Demetras, Post, and Snow [55]) give reason to believe that negative information is not systematically available to the learner. Other studies (e.g., Newport, Gleitman, and Gleitman [136] and Schieffelin and Eisenberg [168]) underline the relative insensitivity of the acquisition process to variations in the order in which language is addressed to children. And Lenneberg [125] describes clinical cases revealing that a child's own linguistic productions are not essential to his or her mastery of an incoming language. For further discussion, see Pinker [148].

		§3.3 Language Identification: Scientists

		We turn to 3.1d, the concept of scientist in the present model. The following notation will be used here and later.

		3.6 Definition

		(a) Let text T and be given. The nth member oft is denoted by T(n). The initial finite sequence of T of length n is denoted T[n].

		(b) The set is denoted by SEQ;  s , ,  g  are variables over SEQ.

		(c) Let be given. The length of  s  is denoted by . The unique with is denoted . The set of numbers appearing in  s  is denoted by content( s ). For , the nth member of  s  is denoted by  s (n), and the initial sequence of length n in  s  is denoted by  s [n].

		For example, if T is the text of 3.5, then T(2) = #, T[5] = 0, 0, #, #, 2, and content(T[5]) = {0, 2}. We note the following facts about this notation.

		3.7 Lemma Let text T and be given.

		(a) The "first" member oft is T(0); T(1) is the second member.

		(b) T[n] does not extend to T(n), so content(T[n]) does not in general include T(n). (For example, if T is 3.5, then 2 content(T[4]).)