by Jean Barbet | Apr 16, 2024 | Algebra, Functions, Non classé
Polynomials with one variable are mathematical representations of the expressions used in polynomial equations. They allow algebraic methods to be applied to solving these equations. 1. Equations are “linguistic” objects 1.1 Polynomial equations and number...
by Jean Barbet | Jul 9, 2023 | Logic, Number Theory, Set Theory
Natural arithmetic is the science of natural numbers: it is based on addition, multiplication, natural order and divisibility. Now, all these operations and relations are defined on the basis of the single successor function, whose properties are brought together in...
by Jean Barbet | May 29, 2021 | Logic, Set Theory
Russell’s paradox or antinomy is a very simple paradox in naive set theory, which arises when one tries to define a “set of all sets”. Its resolution relies on the introduction of the notion of class and the distinction of sets among classes. Thanks...
by Jean Barbet | May 23, 2021 | Algebra, Geometry
The linear transformations of the Euclidean plane are the invertible linear applications, i.e. of non-zero determinant. They allow us to move from one basis of the plane to another, and the orthogonal transformations, i.e. the vectorial isometries, exchange the...
by Jean Barbet | May 8, 2021 | Algebra, Geometry, Non classé
The representation of the Euclidean plane as the Cartesian product \(\mathbb R^2\) allows us to decompose any vector of the plane into two coordinates, its abscissa and its ordinate. This decomposition is linked to a particular and natural “representation...