533,978 research outputs found
Recursión, inducción y órdenes bien fundados
Con base en la caracterización de los números naturales a partir de la propiedad de recursión (ver [2]), probamos en forma general que para un conjunto dado las propiedades de recursión, inducción y buena fundación son equivalentes entre sí. El resultado lo extendemos a clases y lo utilizamos para dar otra prueba de la caracterización del conjunto de los naturales mediante recursión.
Based on the characterization of the set of natural numbers by the recursion property, developed in [2], we prove in a general setting that the properties of recursion, induction and well-foundedness are equivalent for a given set. This result is extended to classes and is used to give another proof of the characterization of the set of natural numbers by recursion
Sharp bounds for higher linear syzygies and classifications of projective varieties
In the present paper, we consider upper bounds of higher linear syzygies i.e.
graded Betti numbers in the first linear strand of the minimal free resolutions
of projective varieties in arbitrary characteristic. For this purpose, we first
remind `Partial Elimination Ideals (PEIs)' theory and introduce a new framework
in which one can study the syzygies of embedded projective schemes well using
PEIs theory and the reduction method via inner projections.
Next we establish fundamental inequalities which govern the relations between
the graded Betti numbers in the first linear strand of an algebraic set and
those of its inner projection . Using these results, we obtain some
natural sharp upper bounds for higher linear syzygies of any nondegenerate
projective variety in terms of the codimension with respect to its own
embedding and classify what the extremal case and next-to-extremal case are.
This is a generalization of Castelnuovo and Fano's results on the number of
quadrics containing a given variety and another characterization of varieties
of minimal degree and del Pezzo varieties from the viewpoint of `syzygies'.
Note that our method could be also applied to get similar results for more
general categories (e.g. connected in codimension one algebraic sets).Comment: 22 pages, 7 figures, comments are welcome
Characterization theorem for the conditionally computable real functions
The class of uniformly computable real functions with respect to a small
subrecursive class of operators computes the elementary functions of calculus,
restricted to compact subsets of their domains. The class of conditionally
computable real functions with respect to the same class of operators is a
proper extension of the class of uniformly computable real functions and it
computes the elementary functions of calculus on their whole domains. The
definition of both classes relies on certain transformations of infinitistic
names of real numbers. In the present paper, the conditional computability of
real functions is characterized in the spirit of Tent and Ziegler, avoiding the
use of infinitistic names
Inductive reasoning in the justification of the result of adding two even numbers
In this paper we present an analysis of the inductive reasoning of twelve secondary students in a mathematical problem-solving context. Students were proposed to justify what is the result of adding two even numbers. Starting from the theoretical framework, which is based on Pólya’s stages of inductive reasoning, and our empirical work, we created a category system that allowed us to make a qualitative data analysis. We show in this paper some of the results obtained in a previous study
The Finite and the Infinite in Frege's Grundgesetze der Arithmetik
Discusses Frege's formal definitions and characterizations of infinite and finite sets. Speculates that Frege might have discovered the "oddity" in Dedekind's famous proof that all infinite sets are Dedekind infinite and, in doing so, stumbled across an axiom of countable choice
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