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26 de mar. de 2024 · Resumen. En el presente artículo analizamos los aportes decisivos de tres miembros de la escuela alemana de matemática a la separación del concepto de número de la idea física de magnitud, durante la segunda mitad del siglo XIX.
Hace 1 día · Richard Dedekind: el precursor del enfoque estructuralista de la matemática 03 enero, 2022 Estableció formalmente la continuidad de la recta real, definiendo un número real por medio de un dispositivo llamado cortadura.
23 de mar. de 2024 · After the important foundational work of Cantor, Richard Dedekind (1831–1916), and Weierstrass, infinitesimals were seen by mathematicians as both unnecessary and unworkable. This did not prevent physicists and engineers from freely using infinitesimals and enjoying their great convenience.
12 de abr. de 2024 · Galileo concluded that “we cannot speak of infinite quantities as being the one greater or less than or equal to another.” Such examples led the German mathematician Richard Dedekind in 1872 to suggest a definition of an infinite set as one that could be put in a one-to-one relationship with some proper subset.
Hace 6 días · An integral domain is called a Dedekind domain if for each pair of ideals , there is an ideal such that =. It can then be shown that every nonzero ideal of a Dedekind domain can be uniquely written as a product of maximal ideals, a generalization of the fundamental theorem of arithmetic .
5 de abr. de 2024 · Richard Dedekind instead defined an infinite set as one that has the same number of elements as a proper subset of itself; that is, a set that you can remove at least one or more elements from and still have as many elements as before. This is today called Dedekind-Infinite.
Hace 1 día · We will use \ ( {\mathbb {R}}\) as the name for the set of all Dedekind cuts. To make the set \ ( {\mathbb {R}}\) a number structure, we need to say how the Dedekind cuts are added and multiplied. We will only define addition. This definition of multiplication is similar, but more complicated.
