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Set theory

Number theory
Set theory
August 15, 20210Comments

What is a real number ? Cauchy’s fantastic construction

The real numbers are all the "quantities" that we can order, and we can "construct" them in various ways thanks to set theory. "Numbers govern the world." Pythagoras The real numbers idealise
Middle point of a rational segment
Number theory
Set theory
August 6, 20210Comments

What is a rational number? Quotients of numbers and sets

1.The intuition of rational numbers Rational numbers, i.e. "fractional" numbers, such as \(-\frac 1 2, \frac{27}{4}, \frac{312}{-6783},\ldots\), form an intuitive set which we note \(\mathbb Q\). It is an extension of
Construction of the set of integers
Number theory
Set theory
July 30, 20210Comments

What is an integer ? A crafty representation

Integers are an extension of the natural numbers where the existence of subtraction provides a more appropriate framework for certain questions of arithmetic. They can be described axiomatically, but can
Natural numbers
Number theory
Set theory
July 30, 20210Comments

What is a natural number? Defining or axiomatising

Mathematical science does not seek to define the notion of a natural number, but to understand the set of natural numbers. "Natural numbers have been made by God, everything else is
Ulam spiral
Number theory
Set theory
July 17, 20210Comments

An infinity of prime numbers : Euclid’s theorem

The prime natural numbers are those which have no divisors other than 1 and themselves. They exist in infinite number by Euclid's theorem, which is not difficult to prove. 1.Prime numbers 1.1.Divisors
Bijection between finite sets
Functions
Set theory
July 17, 20210Comments

Finiteness and Mathematical Infinity : Comparing and Enumerating

A finite set is a set that can be counted using the natural numbers \(1,\ldots,n\) for a certain natural number \(n\). But what is counting ? And then, what is
Subsets of a 3 elements set
Set theory
July 2, 20210Comments

What is a set? Founding mathematics in intuition

Naive set theory or "potato science" is the natural (and understandable!) foundation of mathematical science. "I know what time is. If you ask me, I don't know anymore." Augustine. This insightful quote

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