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the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty...

an axiom is a premise or starting point for reasoning. In mathematics, an axiom may be a "logical axiom" or a "non-logical axiom". Logical axioms are...

In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty...

theory, the axiom of union is one of the axioms of Zermelo–Fraenkel set theory. This axiom was introduced by Ernst Zermelo. Informally, the axiom states that...

where C stands for "choice", and ZF refers to the axioms of Zermelo–Fraenkel set theory with the axiom of choice excluded. Informally, Zermelo–Fraenkel set...

theory and the branches of logic, mathematics, and computer science that use it, the axiom of pairing is one of the axioms of Zermelo–Fraenkel set theory...

Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie (tr. The Foundations of Geometry)...

1964, p. 100 axiom II.5 in Hilbert's Foundations of Geometry (Townsend translation referenced below), in the authorized English translation of the 10th edition...

mathematical logic, the Peano axioms (/piˈɑːnoʊ/, [peˈaːno]), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers...

set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any...

1929 axiom system, which contains all the axioms of his 1925 axiom system except the axiom of limitation of size. He replaced this axiom with two of its...

Freiling's axiom of symmetry ( AX {\displaystyle {\texttt {AX}}} ) is a set-theoretic axiom proposed by Chris Freiling. It is based on intuition of Stuart...

the axiom of limitation of size was proposed by John von Neumann in his 1925 axiom system for sets and classes. It formalizes the limitation of size...

or right translation by ⁠ a {\displaystyle a} ⁠. The group axioms for identity and inverses may be "weakened" to assert only the existence of a left identity...

foundation axiom of ZFC is replaced by axioms implying its negation. The study of non-well-founded sets was initiated by Dmitry Mirimanoff in a series of papers...

original axioms, with the original text (translated into English) and original numbering. The axioms of Zermelo set theory are stated for objects, some of which...

Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to...

assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results...

revealed the existence of non-Desarguesian planes, examples to show that the axioms of incidence can be modelled (in two dimensions only) by structures not accessible...

class of cardinals which satisfy a predicate of interest. In the case of inaccessibility, the corresponding axiom is the assertion that for every cardinal...

Lost in Translation may refer to: Look up lost in translation in Wiktionary, the free dictionary. Lost in Translation (film), a 2003 film directed by...