by Jean Barbet | Aug 20, 2020 | Algebra, Non classé
There are various ways of defining complex numbers. The most direct way is to look at them as points or vectors of the Euclidean plane. Addition and multiplication are then defined using the coordinates. 1. The set \(\mathbb C\) of complex numbers 1.1. A complex... 
by Jean Barbet | Jul 10, 2020 | Functions, Set Theory
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 an infinite set? 1.Comparing sets : the notion of bijection The notions of finite set and infinite set, and... 
by Jean Barbet | Jul 6, 2020 | Functions, Geometry
The definition of a circle is simple: it is a set of points located at the same distance from a given point. This distance is called the radius and this point is called the centre of the circle. The circle with centre \((-1,-3/2)\) and radius \(\sqrt 6\) 1. Circles as... 
by Jean Barbet | Jul 1, 2020 | Algebra, Geometry
From Descartes’ analytic approach, which consists in introducing coordinates to represent the points of the plane, and from Cauchy’s construction of the real numbers, we can give a modern representation of the euclidean plane from which we recover... 
by Jean Barbet | Jun 25, 2020 | Functions, Geometry
The derivative of a function is its instantaneous variation, i.e. the slope of the tangent to the graphical representation of the function at that point. 1. General idea: an instantaneous variation We place ourselves here in the framework of functions of a real...