例句與造句

1. The first level of the Levy hierarchy is defined as containing only formulas with no unbounded quantifiers, and is denoted by \ Delta _ 0 = \ Sigma _ 0 = \ Pi _ 0.
2. Thus there is a formula \ varphi ( n, n _ 1 ) in first-order arithmetic with no unbounded quantifiers, such that T halts on input n at time n 1 at most if and only if \ varphi ( n, n _ 1 ) is satisfied.
3. Prefix induction can simulate predecessor induction, but only at the cost of making the statement more syntactically complex ( adding a bounded universal quantifier ), so the interesting results relating prefix induction to polynomial-time computation depend on excluding unbounded quantifiers entirely, and limiting the alternation of bounded universal and existential quantifiers allowed in the statement.
4. The consequent most immediate challenge in Geometry is to  correct Euclid by establishing the theorems of Book VI on the basis of the methods and techniques of Books I-IV, avoiding the use of the ratio concept introduced in Book V . For Arithmetic the corresponding challenge is to establish the results of Book VII-IX without resort to the sort of iterative procedure that Euclid allows himself in the definition of multiplication . ( Book VII, Definition 15 . ) For Cantorian Arithmetic the main challenge would be to show that the great body of infinitary mathematics-the disciplines flowing in one way or another from the calculus-does not require unbounded quantifiers and consequently that the instances of the Replacement Schema of the Zermelo-Fraenkel axioms for set theory involving such quantifiers, are, as well as being disallowed by Mayberry s general philosophy, in any case technically redundant.
5. It's difficult to find unbounded quantifier in a sentence. 用unbounded quantifier造句挺難的