Abstract
The aim of this paper is to use some concepts of nonstandard analysis given by Robinson, A. and axiomataized by Nelson, E. to prove some theorems concerning the approximation of integrals and the convergence of sequences and series.
Highlights
Through this paper we consider properties of a quite general nature, which unify certain number of processes used to establish approximate expression of numbers and functions.we shall explain our nonstandard works and we treat the following problems. a)How to approximate certain functions to other functions? b)How to calculate the proper and improper integrals for approximate functions?Tahher H
We form a condition in order that the approximate equality of Theorem (I.1) holds for unbounded intervals
First of all we observe that Theorem (I.2) is mainly concerned with the functions f, which are: i) Limited every where, ii) noninfinitesimals on a subset of R, which contains at least one interval of appreciable length, and does not exceed the principal galaxy[2]
Summary
Through this paper we consider properties of a quite general nature, which unify certain number of processes used to establish approximate expression of numbers and functions.we shall explain our nonstandard works and we treat the following problems. a)How to approximate certain functions to other functions? b)How to calculate the proper and improper integrals for approximate functions?Tahher H. A real number x is called limited if x r for some r R + . A real number x is called appreciable (denoted by A+ ), if x is limited but not infinitesimal.
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