by M4t_6_onL | Jan 28, 2022 | 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 M4t_6_onL | Sep 13, 2021 | 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 M4t_6_onL | Aug 15, 2021 | Number theory, Set theory
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 all the “points” of the...
by M4t_6_onL | Aug 6, 2021 | Number theory, Set theory
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 the set \(\mathbb Z\) of integers (see...
by M4t_6_onL | Jul 30, 2021 | Number theory, Set theory
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 also be constructed from the set of natural numbers and some...