- Dedekind axiom
- матем.аксиома Дедекинда, принцип Дедекинда
English-Russian scientific dictionary. 2008.
Dedekind axiom
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Cantor-Dedekind axiom — The phrase Cantor Dedekind axiom has been used to describe the thesis that the real numbers are order isomorphic to the linear continuum of geometry. In other words the axiom states that there is a one to one correspondence between real numbers… … Wikipedia
Dedekind-infinite set — In mathematics, a set A is Dedekind infinite if some proper subset B of A is equinumerous to A. Explicitly, this means that there is a bijective function from A onto some proper subset B of A. A set is Dedekind finite if it is not Dedekind… … Wikipedia
Axiom of countable choice — The axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory, similar to the axiom of choice. It states that any countable collection of non empty sets must have a choice function. Spelled out, this means… … Wikipedia
Axiom of choice — This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band). In mathematics, the axiom of choice, or AC, is an axiom of set theory stating that for every family of nonempty sets there exists a family of … Wikipedia
Axiom — This article is about logical propositions. For other uses, see Axiom (disambiguation). In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self evident or to define and… … Wikipedia
Peano-Axiom — ℕ Die natürlichen Zahlen sind die beim Zählen verwendeten Zahlen 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 usw. Oft wird auch die 0 (Null) zu den natürlichen Zahlen gerechnet. Sie bilden bezüglich der Addition und der Multiplikation einen (additiv und… … Deutsch Wikipedia
Completeness axiom — In mathematics the completeness axiom, also called Dedekind completeness of the real numbers, is a fundamental property of the set R of real numbers. It is the property that distinguishes R from other ordered fields, especially from the set of… … Wikipedia
Richard Dedekind — Infobox Scientist name = PAGENAME box width = image size =180px caption =Richard Dedekind, c. 1850 birth date = October 6, 1831 birth place = Braunschweig death date = February 12, 1916 death place = Braunschweig residence = citizenship =… … Wikipedia
Least upper bound axiom — The least upper bound axiom, also abbreviated as the LUB axiom, is an axiom of real analysis stating that if a nonempty subset of the real numbers has an upper bound, then it has a least upper bound. It is an axiom in the sense that it cannot be… … Wikipedia
Hilbert's program — Hilbert s program, formulated by German mathematician David Hilbert in the 1920s, was to formalize all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent.Hilbert proposed that the… … Wikipedia
Analytic geometry — Cartesian coordinates. Analytic geometry, or analytical geometry has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties. This article focuses on the classical and elementary meaning … Wikipedia
