Search results
Results From The WOW.Com Content Network
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα (axíōma), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.
Together with the axiom of choice (see below), these are the de facto standard axioms for contemporary mathematics or set theory. They can be easily adapted to analogous theories, such as mereology. Axiom of extensionality; Axiom of empty set; Axiom of pairing; Axiom of union; Axiom of infinity; Axiom schema of replacement; Axiom of power set ...
The Normal Moore Space conjecture, namely that every normal Moore space is metrizable, can be disproven assuming the continuum hypothesis or assuming both Martin's axiom and the negation of the continuum hypothesis, and can be proven assuming a certain axiom which implies the existence of large cardinals. Thus, granted large cardinals, the ...
One such problem was the continuum hypothesis. Zermelo–Fraenkel set theory, with the historically controversial axiom of choice included, is commonly abbreviated ZFC, where "C" stands for "choice". Many authors use ZF to refer to the axioms of Zermelo–Fraenkel set theory with the axiom of choice excluded. [5]
Axiomatic quantum field theory is a mathematical discipline which aims to describe quantum field theory in terms of rigorous axioms. It is strongly associated with functional analysis and operator algebras, but has also been studied in recent years from a more geometric and functorial perspective.
The axiom of global choice follows from the axiom of limitation of size. Tarski's axiom, which is used in Tarski–Grothendieck set theory and states (in the vernacular) that every set belongs to some Grothendieck universe, is stronger than the axiom of choice.
U.S.-based startup Axiom Space is exploring using Indian launch vehicles to support its international space station mission, a senior executive said on Tuesday.
Protein folding problem: Is it possible to predict the secondary, tertiary and quaternary structure of a polypeptide sequence based solely on the sequence and environmental information? Inverse protein-folding problem: Is it possible to design a polypeptide sequence which will adopt a given structure under certain environmental conditions?