Faster access than browser!
146 relations: Abstract algebra, Alain Aspect, Albert Einstein, Alessandro Padoa, Algebraic topology, Ancient Greece, Ancient philosophy, Angle, Aristotle, Arithmetic, Axiom schema, Axiomatic system, Évariste Galois, Bell's theorem, Bertrand Russell, Boethius, Boolean algebra, Change of variables, Circle, Class (set theory), Commutative property, Complex analysis, Conservative extension, Consistency, Continuum hypothesis, Copenhagen interpretation, Corollary, David Hilbert, Deductive reasoning, Determinism, Differential geometry, Differential topology, Discourse, Dogma, Elliptic geometry, EPR paradox, Ergodic theory, Euclid, Euclid's Elements, Euclidean geometry, Falsifiability, Field (mathematics), First-order logic, Forcing (mathematics), Formal language, Formal system, Foundations of geometry, Free variables and bound variables, Galois theory, Gödel's completeness theorem, ..., Gödel's incompleteness theorems, Geminus, General relativity, General topology, Geometry, Georg Cantor, Giuseppe Peano, Gottlob Frege, Greek language, Grothendieck universe, Group (mathematics), Group theory, Henri Poincaré, Homology (mathematics), Homotopy, Hyperbolic geometry, Inaccessible cardinal, Infinite set, Integer, Isaac Newton, Isomorphism, John Stewart Bell, Kurt Gödel, Löwenheim–Skolem theorem, Line (geometry), Line–line intersection, List of axioms, Logic, Logical connective, Logical consequence, Logical truth, Logicism, Mario Pieri, Mathematical logic, Mathematical theory, Mathematician, Mathematics, Measure (mathematics), Model theory, Modus ponens, Morse–Kelley set theory, Naive set theory, Natural number, Negation, Niels Bohr, Non-standard analysis, Number theory, Parallel postulate, Paul Cohen, Peano axioms, Philosopher, Philosophy of mathematics, Polygon, Posterior Analytics, Premise, Presupposition, Primitive notion, Probability, Probability theory, Proclus, Propositional calculus, Propositional variable, Quantum mechanics, Real analysis, Real number, Regulæ Juris, Representation theory, Right angle, Ring (mathematics), Rule of inference, Russell's paradox, Satisfiability, Science, Second-order arithmetic, Second-order logic, Self-evidence, Set theory, Space, Spacetime, Special relativity, Successor function, Syllogism, Tautology (logic), Theorem, Theoretical physics, Thomas Little Heath, Topological space, Triangle, Truth, Unary function, Valuation (logic), Vector space, Verbal noun, Von Neumann–Bernays–Gödel set theory, Well-formed formula, Zermelo–Fraenkel set theory. Expand index (96 more) »
Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
New!!: Axiom and Abstract algebra · See more »
Alain Aspect
Alain Aspect (born 15 June 1947) is a French physicist noted for his experimental work on quantum entanglement.
New!!: Axiom and Alain Aspect · See more »
Albert Einstein
Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).
New!!: Axiom and Albert Einstein · See more »
Alessandro Padoa
Alessandro Padoa (14 October 1868 – 25 November 1937) was an Italian mathematician and logician, a contributor to the school of Giuseppe Peano.
New!!: Axiom and Alessandro Padoa · See more »
Algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.
New!!: Axiom and Algebraic topology · See more »
Ancient Greece
Ancient Greece was a civilization belonging to a period of Greek history from the Greek Dark Ages of the 13th–9th centuries BC to the end of antiquity (AD 600).
New!!: Axiom and Ancient Greece · See more »
Ancient philosophy
This page lists some links to ancient philosophy.
New!!: Axiom and Ancient philosophy · See more »
Angle
In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
New!!: Axiom and Angle · See more »
Aristotle
Aristotle (Ἀριστοτέλης Aristotélēs,; 384–322 BC) was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, in the north of Classical Greece.
New!!: Axiom and Aristotle · See more »
Arithmetic
Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.
New!!: Axiom and Arithmetic · See more »
Axiom schema
In mathematical logic, an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom.
New!!: Axiom and Axiom schema · See more »
Axiomatic system
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.
New!!: Axiom and Axiomatic system · See more »
Évariste Galois
Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician.
New!!: Axiom and Évariste Galois · See more »
Bell's theorem
Bell's theorem is a "no-go theorem" that draws an important distinction between quantum mechanics and the world as described by classical mechanics.
New!!: Axiom and Bell's theorem · See more »
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.
New!!: Axiom and Bertrand Russell · See more »
Boethius
Anicius Manlius Severinus Boëthius, commonly called Boethius (also Boetius; 477–524 AD), was a Roman senator, consul, magister officiorum, and philosopher of the early 6th century.
New!!: Axiom and Boethius · See more »
Boolean algebra
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.
New!!: Axiom and Boolean algebra · See more »
Change of variables
In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables.
New!!: Axiom and Change of variables · See more »
Circle
A circle is a simple closed shape.
New!!: Axiom and Circle · See more »
Class (set theory)
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share.
New!!: Axiom and Class (set theory) · See more »
Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
New!!: Axiom and Commutative property · See more »
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
New!!: Axiom and Complex analysis · See more »
Conservative extension
In mathematical logic, a conservative extension is a supertheory of a theory which is often convenient for proving theorems, but proves no new theorems about the language of the original theory.
New!!: Axiom and Conservative extension · See more »
Consistency
In classical deductive logic, a consistent theory is one that does not contain a contradiction.
New!!: Axiom and Consistency · See more »
Continuum hypothesis
In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets.
New!!: Axiom and Continuum hypothesis · See more »
Copenhagen interpretation
The Copenhagen interpretation is an expression of the meaning of quantum mechanics that was largely devised in the years 1925 to 1927 by Niels Bohr and Werner Heisenberg.
New!!: Axiom and Copenhagen interpretation · See more »
Corollary
A corollary is a statement that follows readily from a previous statement.
New!!: Axiom and Corollary · See more »
David Hilbert
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.
New!!: Axiom and David Hilbert · See more »
Deductive reasoning
Deductive reasoning, also deductive logic, logical deduction is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion.
New!!: Axiom and Deductive reasoning · See more »
Determinism
Determinism is the philosophical theory that all events, including moral choices, are completely determined by previously existing causes.
New!!: Axiom and Determinism · See more »
Differential geometry
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.
New!!: Axiom and Differential geometry · See more »
Differential topology
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds.
New!!: Axiom and Differential topology · See more »
Discourse
Discourse (from Latin discursus, "running to and from") denotes written and spoken communications.
New!!: Axiom and Discourse · See more »
Dogma
The term dogma is used in pejorative and non-pejorative senses.
New!!: Axiom and Dogma · See more »
Elliptic geometry
Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.
New!!: Axiom and Elliptic geometry · See more »
EPR paradox
The Einstein–Podolsky–Rosen paradox or the EPR paradox of 1935 is a thought experiment in quantum mechanics with which Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen (EPR) claimed to demonstrate that the wave function does not provide a complete description of physical reality, and hence that the Copenhagen interpretation is unsatisfactory; resolutions of the paradox have important implications for the interpretation of quantum mechanics.
New!!: Axiom and EPR paradox · See more »
Ergodic theory
Ergodic theory (Greek: έργον ergon "work", όδος hodos "way") is a branch of mathematics that studies dynamical systems with an invariant measure and related problems.
New!!: Axiom and Ergodic theory · See more »
Euclid
Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".
New!!: Axiom and Euclid · See more »
Euclid's Elements
The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.
New!!: Axiom and Euclid's Elements · See more »
Euclidean geometry
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
New!!: Axiom and Euclidean geometry · See more »
Falsifiability
A statement, hypothesis, or theory has falsifiability (or is falsifiable) if it can logically be proven false by contradicting it with a basic statement.
New!!: Axiom and Falsifiability · See more »
Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
New!!: Axiom and Field (mathematics) · See more »
First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
New!!: Axiom and First-order logic · See more »
Forcing (mathematics)
In the mathematical discipline of set theory, forcing is a technique for proving consistency and independence results.
New!!: Axiom and Forcing (mathematics) · See more »
Formal language
In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols together with a set of rules that are specific to it.
New!!: Axiom and Formal language · See more »
Formal system
A formal system is the name of a logic system usually defined in the mathematical way.
New!!: Axiom and Formal system · See more »
Foundations of geometry
Foundations of geometry is the study of geometries as axiomatic systems.
New!!: Axiom and Foundations of geometry · See more »
Free variables and bound variables
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation that specifies places in an expression where substitution may take place.
New!!: Axiom and Free variables and bound variables · See more »
Galois theory
In the field of algebra within mathematics, Galois theory, provides a connection between field theory and group theory.
New!!: Axiom and Galois theory · See more »
Gödel's completeness theorem
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic.
New!!: Axiom and Gödel's completeness theorem · See more »
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.
New!!: Axiom and Gödel's incompleteness theorems · See more »
Geminus
Geminus of Rhodes (Γεμῖνος ὁ Ῥόδιος), was a Greek astronomer and mathematician, who flourished in the 1st century BC.
New!!: Axiom and Geminus · See more »
General relativity
General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
New!!: Axiom and General relativity · See more »
General topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.
New!!: Axiom and General topology · See more »
Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
New!!: Axiom and Geometry · See more »
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.
New!!: Axiom and Georg Cantor · See more »
Giuseppe Peano
Giuseppe Peano (27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist.
New!!: Axiom and Giuseppe Peano · See more »
Gottlob Frege
Friedrich Ludwig Gottlob Frege (8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician.
New!!: Axiom and Gottlob Frege · See more »
Greek language
Greek (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean and the Black Sea.
New!!: Axiom and Greek language · See more »
Grothendieck universe
In mathematics, a Grothendieck universe is a set U with the following properties.
New!!: Axiom and Grothendieck universe · See more »
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
New!!: Axiom and Group (mathematics) · See more »
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
New!!: Axiom and Group theory · See more »
Henri Poincaré
Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.
New!!: Axiom and Henri Poincaré · See more »
Homology (mathematics)
In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
New!!: Axiom and Homology (mathematics) · See more »
Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
New!!: Axiom and Homotopy · See more »
Hyperbolic geometry
In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.
New!!: Axiom and Hyperbolic geometry · See more »
Inaccessible cardinal
In set theory, an uncountable cardinal is inaccessible if it cannot be obtained from smaller cardinals by the usual operations of cardinal arithmetic.
New!!: Axiom and Inaccessible cardinal · See more »
Infinite set
In set theory, an infinite set is a set that is not a finite set.
New!!: Axiom and Infinite set · See more »
Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
New!!: Axiom and Integer · See more »
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.
New!!: Axiom and Isaac Newton · See more »
Isomorphism
In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.
New!!: Axiom and Isomorphism · See more »
John Stewart Bell
John Stewart Bell FRS (28 June 1928 – 1 October 1990) was a Northern Irish physicist, and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden variable theories.
New!!: Axiom and John Stewart Bell · See more »
Kurt Gödel
Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.
New!!: Axiom and Kurt Gödel · See more »
Löwenheim–Skolem theorem
In mathematical logic, the Löwenheim–Skolem theorem, named for Leopold Löwenheim and Thoralf Skolem, states that if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The result implies that first-order theories are unable to control the cardinality of their infinite models, and that no first-order theory with an infinite model can have a unique model up to isomorphism.
New!!: Axiom and Löwenheim–Skolem theorem · See more »
Line (geometry)
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.
New!!: Axiom and Line (geometry) · See more »
Line–line intersection
In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or a line.
New!!: Axiom and Line–line intersection · See more »
List of axioms
This is a list of axioms as that term is understood in mathematics, by Wikipedia page.
New!!: Axiom and List of axioms · See more »
Logic
Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.
New!!: Axiom and Logic · See more »
Logical connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the value of the compound sentence produced depends only on that of the original sentences and on the meaning of the connective.
New!!: Axiom and Logical connective · See more »
Logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
New!!: Axiom and Logical consequence · See more »
Logical truth
Logical truth is one of the most fundamental concepts in logic, and there are different theories on its nature.
New!!: Axiom and Logical truth · See more »
Logicism
Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic.
New!!: Axiom and Logicism · See more »
Mario Pieri
Mario Pieri (22 June 1860 – 1 March 1913) was an Italian mathematician who is known for his work on foundations of geometry.
New!!: Axiom and Mario Pieri · See more »
Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
New!!: Axiom and Mathematical logic · See more »
Mathematical theory
A mathematical theory is a subfield of mathematics that is an area of mathematical research.
New!!: Axiom and Mathematical theory · See more »
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
New!!: Axiom and Mathematician · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Axiom and Mathematics · See more »
Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.
New!!: Axiom and Measure (mathematics) · See more »
Model theory
In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.
New!!: Axiom and Model theory · See more »
Modus ponens
In propositional logic, modus ponens (MP; also modus ponendo ponens (Latin for "mode that affirms by affirming") or implication elimination) is a rule of inference.
New!!: Axiom and Modus ponens · See more »
Morse–Kelley set theory
In the foundations of mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of Quine and Morse is a first order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG).
New!!: Axiom and Morse–Kelley set theory · See more »
Naive set theory
Naïve set theory is any of several theories of sets used in the discussion of the foundations of mathematics.
New!!: Axiom and Naive set theory · See more »
Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
New!!: Axiom and Natural number · See more »
Negation
In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P (¬P), which is interpreted intuitively as being true when P is false, and false when P is true.
New!!: Axiom and Negation · See more »
Niels Bohr
Niels Henrik David Bohr (7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922.
New!!: Axiom and Niels Bohr · See more »
Non-standard analysis
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.
New!!: Axiom and Non-standard analysis · See more »
Number theory
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
New!!: Axiom and Number theory · See more »
Parallel postulate
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry.
New!!: Axiom and Parallel postulate · See more »
Paul Cohen
Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician.
New!!: Axiom and Paul Cohen · See more »
Peano axioms
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.
New!!: Axiom and Peano axioms · See more »
Philosopher
A philosopher is someone who practices philosophy, which involves rational inquiry into areas that are outside either theology or science.
New!!: Axiom and Philosopher · See more »
Philosophy of mathematics
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and purports to provide a viewpoint of the nature and methodology of mathematics, and to understand the place of mathematics in people's lives.
New!!: Axiom and Philosophy of mathematics · See more »
Polygon
In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.
New!!: Axiom and Polygon · See more »
Posterior Analytics
The Posterior Analytics (Ἀναλυτικὰ Ὕστερα; Analytica Posteriora) is a text from Aristotle's Organon that deals with demonstration, definition, and scientific knowledge.
New!!: Axiom and Posterior Analytics · See more »
Premise
A premise or premiss is a statement that an argument claims will induce or justify a conclusion.
New!!: Axiom and Premise · See more »
Presupposition
In the branch of linguistics known as pragmatics, a presupposition (or PSP) is an implicit assumption about the world or background belief relating to an utterance whose truth is taken for granted in discourse.
New!!: Axiom and Presupposition · See more »
Primitive notion
In mathematics, logic, and formal systems, a primitive notion is an undefined concept.
New!!: Axiom and Primitive notion · See more »
Probability
Probability is the measure of the likelihood that an event will occur.
New!!: Axiom and Probability · See more »
Probability theory
Probability theory is the branch of mathematics concerned with probability.
New!!: Axiom and Probability theory · See more »
Proclus
Proclus Lycaeus (8 February 412 – 17 April 485 AD), called the Successor (Greek Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major classical philosophers (see Damascius).
New!!: Axiom and Proclus · See more »
Propositional calculus
Propositional calculus is a branch of logic.
New!!: Axiom and Propositional calculus · See more »
Propositional variable
In mathematical logic, a propositional variable (also called a sentential variable or sentential letter) is a variable which can either be true or false.
New!!: Axiom and Propositional variable · See more »
Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
New!!: Axiom and Quantum mechanics · See more »
Real analysis
In mathematics, real analysis is the branch of mathematical analysis that studies the behavior of real numbers, sequences and series of real numbers, and real-valued functions.
New!!: Axiom and Real analysis · See more »
Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
New!!: Axiom and Real number · See more »
Regulæ Juris
Regulæ Juris, also spelled as Regulae - and - Iuris is a generic term for general rules or principles serving chiefly for the interpretation of canon laws.
New!!: Axiom and Regulæ Juris · See more »
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.
New!!: Axiom and Representation theory · See more »
Right angle
In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn.
New!!: Axiom and Right angle · See more »
Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
New!!: Axiom and Ring (mathematics) · See more »
Rule of inference
In logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).
New!!: Axiom and Rule of inference · See more »
Russell's paradox
In the foundations of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction.
New!!: Axiom and Russell's paradox · See more »
Satisfiability
In mathematical logic, satisfiability and validity are elementary concepts of semantics.
New!!: Axiom and Satisfiability · See more »
Science
R. P. Feynman, The Feynman Lectures on Physics, Vol.1, Chaps.1,2,&3.
New!!: Axiom and Science · See more »
Second-order arithmetic
In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets.
New!!: Axiom and Second-order arithmetic · See more »
Second-order logic
In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic.
New!!: Axiom and Second-order logic · See more »
Self-evidence
In epistemology (theory of knowledge), a self-evident proposition is a proposition that is known to be true by understanding its meaning without proof, and/or by ordinary human reason.
New!!: Axiom and Self-evidence · See more »
Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
New!!: Axiom and Set theory · See more »
Space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction.
New!!: Axiom and Space · See more »
Spacetime
In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.
New!!: Axiom and Spacetime · See more »
Special relativity
In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.
New!!: Axiom and Special relativity · See more »
Successor function
In mathematics, the successor function or successor operation is a primitive recursive function S such that S(n).
New!!: Axiom and Successor function · See more »
Syllogism
A syllogism (συλλογισμός syllogismos, "conclusion, inference") is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.
New!!: Axiom and Syllogism · See more »
Tautology (logic)
In logic, a tautology (from the Greek word ταυτολογία) is a formula or assertion that is true in every possible interpretation.
New!!: Axiom and Tautology (logic) · See more »
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms.
New!!: Axiom and Theorem · See more »
Theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.
New!!: Axiom and Theoretical physics · See more »
Thomas Little Heath
Sir Thomas Little Heath (5 October 1861 – 16 March 1940) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer.
New!!: Axiom and Thomas Little Heath · See more »
Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
New!!: Axiom and Topological space · See more »
Triangle
A triangle is a polygon with three edges and three vertices.
New!!: Axiom and Triangle · See more »
Truth
Truth is most often used to mean being in accord with fact or reality, or fidelity to an original or standard.
New!!: Axiom and Truth · See more »
Unary function
A unary function is a function that takes one argument.
New!!: Axiom and Unary function · See more »
Valuation (logic)
In logic and model theory, a valuation can be.
New!!: Axiom and Valuation (logic) · See more »
Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
New!!: Axiom and Vector space · See more »
Verbal noun
A verbal noun is a noun formed from or otherwise corresponding to a verb.
New!!: Axiom and Verbal noun · See more »
Von Neumann–Bernays–Gödel set theory
In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel set theory (ZFC).
New!!: Axiom and Von Neumann–Bernays–Gödel set theory · See more »
Well-formed formula
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language.
New!!: Axiom and Well-formed formula · See more »
Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
New!!: Axiom and Zermelo–Fraenkel set theory · See more »
Redirects here:
Axiomatic, Axiomatical, Axiomatically, Axiomm, Axioms, Axoims, Fundamental postulates, Logical axiom, Logical axioms, Mathematical assumption, Mathematical axiom, Non-logical axioms, Philosophical law, Posit (word), Postulate, Postulated, Postulates, Postulating, Postulation, Postulations, Primitive sentence.
References
[1] https://en.wikipedia.org/wiki/Axiom
