Defining continuity of real functions of real variables

@article{Harper2016DefiningCO,
  title={Defining continuity of real functions of real variables},
  author={John F. Harper},
  journal={BSHM Bulletin: Journal of the British Society for the History of Mathematics},
  year={2016},
  volume={31},
  pages={189 - 204}
}
  • J. Harper
  • Published 11 April 2016
  • Medicine
  • BSHM Bulletin: Journal of the British Society for the History of Mathematics
Continuity of a real function of a real variable has been defined in various ways over almost 200 years. Contrary to popular belief, the definitions are not all equivalent, because their consequences for four somewhat pathological functions reveal five essentially different cases. The four defensible ones imply just two cases for continuity on an interval if that is defined by using pointwise continuity at each point. Some authors had trouble: two different textbooks each gave two arguably… 

On some types of somewhat continuous functions

Abstract Many researchers have introduced several generalizations of somewhat continuous functions. In our paper, we want to define a new type of somewhat continuous function by using the definition

Riemann Zeta Based Surge Modelling of Continuous Real Functions in Electrical Circuits

  • Binesh Thankappan
  • Mathematics
    International Journal of Circuits, Systems and Signal Processing
  • 2022
Riemann zeta is defined as a function of a complex variable that analytically continues the sum of the Dirichlet series, when the real part is greater than unity. In this paper, the Riemann zeta

References

SHOWING 1-10 OF 48 REFERENCES

Cauchy’s Cours d’analyse: An Annotated Translation

On real functions..- On infinitely small and infinitely large quantities, and on the continuity of functions. Singular values of functions in various particular cases..- On symmetric functions and

The Theory of Functions of a Real Variable and the Theory of Fourier's Series

  • G. H.
  • Mathematics
    Nature
  • 1907
IT is imposible to read Dr. Hobson's book without reflecting on the marvellous change that has come over Cambridge mathematics in the last twenty years. Twenty years ago Cambridge mathematics was a

A Course of Pure Mathematics

1. Real variables 2. Functions of real variables 3. Complex numbers 4. Limits of functions of a positive integral variable 5. Limits of functions of a continuous variable: continuous and

The Theory of Functions of a Real Variable and the Theory of Fourier's Series

THE theory of functions of a real variable is a subject of fairly recent date and is necessarily expanding as new theorems are discovered and fresh generalisations effected. On the other hand, the

Principles of mathematical analysis

Chapter 1: The Real and Complex Number Systems Introduction Ordered Sets Fields The Real Field The Extended Real Number System The Complex Field Euclidean Spaces Appendix Exercises Chapter 2: Basic

A Concrete Introduction to Real Analysis

DISCRETE CALCULUS Introduction Proof by Induction A Calculus of Sums and Differences Sums of Powers Problems SELECTED AREA COMPUTATIONS Introduction Areas under Power Function Graphs The Computation

Lectures on the theory of functions of real variables

for the point of inflexion lies beyond the end of the b a r ; viz., a t a distance from the centre equal to ^ l + f ^ / 3 times the halflength. However, b y loading the bar a t the centre the point

A Course of Modern Analysis

TLDR
The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.

Classics of Mathematics

Springer-Verlag began publishing books in higher mathematics in 1920, when the series Grundlehren der mathematischen Wissenschaften, initially conceived as a series of advanced textbooks, was founded

Princeton companion to mathematics

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written