“Real” Analysis Is a Degenerate Case of Discrete Analysis

  title={“Real” Analysis Is a Degenerate Case of Discrete Analysis},
  author={Doron Zeilberger},
There are many ways to divide mathematics into two-culture dichotomies. An important one is the Discrete vs. the Continuous. Until almost the end of the 20th century, the continuous culture was dominant, as can be witnessed by notation. An important family of Banach spaces of continuous functions is denoted by L , with a Capital L, while their discrete analogs are denoted by the lowercase counterpart l. A function of a continuous variable is denoted by f(x), where the continuous output, f , is… 

On finite approximations of topological algebraic systems

The results show that there do not exist arbitrarily accurate computer arithmetics for the reals that are associative rings and it is proved that a locally compact field cannot be approximated arbitrarily closely by finite rings.

The Automatic Central Limit Theorems Generator (and Much More

Why I hate the Continuous and Love the Discrete I have always loved the discrete and hated the continuous. Perhaps it was the trauma of having to go through the usual curriculum of “rigorous” ,

Mathematical Rigor in Applied Mathematics Based on the Nonstandard Analysis

  • E. Gordon
  • Mathematics
    Communications in Computer and Information Science
  • 2021
A new axiomatic of set theory is introduced that includes vague definitions and concepts at the same level of rigor as in modern classical mathematics, which allows to consider some non-rigorous arguments of applied mathematics as rigorous ones and, thus, to be sure that they are consistent.

Extending the vision of Shannon

The arithmetic of N ⊂ Z ⊂ Q ⊂ R can be extended to a graph arithmetic N ⊂ Z ⊂ Q ⊂ R, where N is the semi-ring of finite simple graphs and where Z,Q are integral domains culminating in a Banach


The arithmetic of N ⊂ Z ⊂ Q ⊂ R can be extended to a graph arithmetic N ⊂ Z ⊂ Q ⊂ R, where N is the semi-ring of finite simple graphs and where Z,Q are integral domains culminating in a Banach

Nonstandard Analysis of the Behavior of Ergodic Means of Dynamical Systems on Very Big Finite Probability Spaces

In this chapter we discuss the behavior of ergodic means of discrete time dynamical systems on a very big finite probability space Y (discrete dynamical systems below). The G. Birkhoff Ergodic

Towards a classification of continuity and on the emergence of generality

Towards a Classification of Continuity and On the Emergence of Generality Daniel Rosiak Chairs: Richard A. Lee, Jr., Fernando Zalamea Readers: Peter Steeves, Avery Goldman This dissertation has for

Skew-Product Dynamical Dystems: Applications to Difference Equations

One of the earliest difference equations, the Fibonacci sequence, was introduced in 1202 in “Liberabaci,” a book about the abacus, by the famous Italian Leonardo di Pisa, better known as Fibonacci.

Habilitation à diriger des recherches

  • lecarrer
  • Computer Science
    Revue Mabillon
  • 2019
This memoir for accreditation to supervise research deals with continuous models of computation and defines a continuous model, signal machines, that generates geometrical figures complying strict rules that can be understood as a continuous extension of cellular automata.

On the Practical Interest of Discrete Inverse Pólya and Weibull‐1 Models in Industrial Reliability Studies

This article aims at bringing some light to the practical interest for the reliability engineer in using two discrete models among the most popular: the Inverse Polya distribution (IPD), based on a Polya urn scheme, and the so-called Weibull-1 (W1) model.