منابع مشابه
Numerical computations and mathematical modelling with infinite and infinitesimal numbers
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not related to the non-standard analysis) is used to work with finite, infinite, and infinitesimal numbers numerically. This can be done on a new kind of a computer...
متن کاملNumerical computations with infinite and infinitesimal numbers: Theory and applications
A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this chapter. It is based on the principle ‘The part is less than the whole’ introduced by Ancient Greeks and applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down fini...
متن کاملComputations for Analysis, Geometry and Topology
My research agenda is built on formulating problems in analysis, geometry and topology for a computational realization and conversely, use of computation for formalizing notions in analysis, geometry and topology. The former stems from a motivation to provide solutions for problems in science and engineering using tools of scientific and high performance computing while the latter encapsulates ...
متن کاملfKenzo: A user interface for computations in Algebraic Topology
fKenzo (= f riendly Kenzo) is a graphical user interface providing a user-friendly front-end for the Kenzo system, a Common Lisp program devoted to Algebraic Topology. The fKenzo system provides the user interface itself, an XML intermediary generator-translator and, finally the Kenzo kernel. We describe in this paper the main points of fKenzo, and we explain also the advantages and limitations...
متن کاملThe Infinity Computer and Numerical Computations with Infinite and Infinitesimal Numbers
A new methodology allowing one to execute numerical computations with finite, infinite, and infinitesimal numbers (see [7,9,15]) on a new type of a computer – the Infinity Computer – is introduced (see EU, USA, and Russian patents [8]). A calculator using the Infinity Computer technology is presented during the talk. The new approach is based on the principle ‘The part is less than the whole’ i...
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ژورنال
عنوان ژورنال: Publications mathématiques de l'IHÉS
سال: 1977
ISSN: 0073-8301,1618-1913
DOI: 10.1007/bf02684341