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Showing 1 to 13 of 13 for “"Transfinite"”.
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Transfinite Ordinal Arithmetic
… more current times, an arithmetic of finite and transfinite ordinal numbers is outlined. The concept of a set is outlined and directed to the understanding that an ordinal, a special kind of number, is a particular kind of well-ordered set. From this, the idea of counting ordinals is introduced. …
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The Infinite Ladder in Mathematics: Transfinite Induction
… explores the mathematical proof method of transfinite induction. Transfinite induction is mathematical induction beyond the natural numbers. These numbers are called ordinals, denoted by Greek letters. This thesis will introduce fundamental concepts of set theory, starting from the formal …
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Transfinite Sequences of Axiom Systems for Set Theory
Made available in DSpace on 2014-12-09T22:17:43Z (GMT). No. of bitstreams: 1 6808241.pdf: 1998340 bytes, checksum: d9b52b03ffc0b694a65007e65b1b0a0d (MD5) Previous issue date: 1967
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Algebraic Grid Generation Using Tensor Product B-Splines
… a variation diminishing approximation to the transfinite bilinear interpolant of the function mapping the boundary of the unit square onto the boundary of the grid.</p> <p>The practicality of optimizing the grid by minimizing a functional involving the Jacobian of the grid generation mapping …
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Multiplicity function for functions of bounded variation
… f(x), i.e., when the cardinal number of roots is transfinite, assign the value infinite where it is understood that the range of the multiplicity function is the extended real number system. Banach^1 was the first to relate this function to a continuous function of bounded variation. He realized …
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Mathematical, philosophical, religious and spontaneous students' explanations of the paradox of Achilles and the tortoise
… we will examine the paradox in terms of limits, transfinite numbers and through geometric proofs. Then we will examine some of the philosophical explanations, and how the two views on the structure of matter explain the paradox. Finally we will examine how the concept of infinity is dealt with in …
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The Structure of Models of Second-order Set Theories
… T. Third, I show that there is a hierarchy of transfinite recursion principles ranging in strength from GBC to KM. This hierarchy is ordered first by the complexity of the properties allowed in the recursions and second by the allowed heights of the recursions. Fourth, I investigate the …
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Three dimensional numerical analysis for flow prediction in positive displacement screw machines
… to produce rotor profiles and an analytical transfinite interpolation method with adaptive meshing to obtain a fully structured 3-D numerical mesh, which is directly transferable to a Computational fluid dynamics (CFD) code. Robust calculations can then be performed while allowing for moving, …
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Axiomatization and Incompleteness in Arithmetic and Set Theory
… best modelled by a theory constructed using the transfinite iterated application of a soundness reflection principle to PA. I argue that Feferman's completeness theorem shows this account of the mind to be incompatible with some elementary assumptions in the epistemology of arithmetic. In chapter …
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Ontology and the foundations of mathematics
… the role replacement plays in the formulation of transfinite recursion and the theory of ordinals, and from the fact that it permits us to express and assert the (first-order) content of the modern cumulative view of the set theoretic universe as arrayed in a cumulative hierarchy of levels. …
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Parametric multi-block grid generation and application to adaptive flow simulations
… B-splines, algebraic grid generation based on transfinite interpolation, and elliptic grid generation with harmonicmappings. A central task in the implementation of a grid generation system is the design of a data structure that can serve both as interface to the PDE solver and as flexible tool …