A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities
A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities
复制标题
执行无限量和无穷小量计算的新应用方法
DOI：
10.15388/informatica.2008.231
复制
发表时间：
2008
期刊：
影响因子：
2.9
通讯作者：
Y. Sergeyev
中科院分区：
文献类型：
--
作者：
Y. Sergeyev
本文描述了一种新的计算方法，可用于无限和无穷小的计算。它基于古希腊人提出的“部分小于整体”的原则，适用于所有数字(有限、无限和无穷小)以及所有集合和过程(有限和无限)。结果表明，用有限个符号将有限、无穷和无穷小数记为唯一框架的特例是可能的。新的方法使我们能够引入无限计算机来处理这样的数字(它的模拟器已经实现)。文中给出了处理发散级数、无穷集合和极限的例子。
A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this paper. 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 finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a unique framework. The new methodology has allowed us to introduce the Infinity Computer working with such numbers (its simulator has already been realized). Examples dealing with divergent series, infinite sets, and limits are given.