Phrase Hound found 29 phrases and 5 compound words that contain axiom. The most common are listed below. Open axiom in the live search for definitions, filters, and the full list.
Phrases 29
- axiom of choiceOne of the axioms of set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty; any version of said axiom, for example specifying the cardinality of the number of sets from which choices are …
- axiom of power setThe axiom that the power set of any set exists and is a valid set, which appears in the standard axiomatisation of set theory, ZFC.
- Peano axiomAny of a set of fundamental axioms describing the natural numbers and their relationships.
- axiom of countable choiceA weaker form of the axiom of choice that states that every countable collection of nonempty sets must have a choice function; equivalently, the statement that the direct product of a countable collection of nonempty sets is nonempty.
- axiom of regularityOne of the axioms in axiomatic set theory, equivalent to the statement that every non-empty set contains a member that is disjoint from that set.
- axiom of infinityOne of the axioms in axiomatic set theory that guarantees the existence of an infinite set.
- axiom of unionOne of the axioms in axiomatic set theory, equivalent to the statement that a union exists for any set, containing exactly all the elements contained within the sets within that set.
- axiom of pairingOne of the axioms in axiomatic set theory, equivalent to the statement that if two sets exist, there exists a set with those two sets as its sole elements.
- axiom of extensionalityOne of the axioms in axiomatic set theory, equivalent to the statement that two sets are equal if and only if they contain the same elements.
- axiom schemaA formula in the language of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.
- Luce's choice axiomAn axiom stating that the relative odds of selecting one item over another from a pool of many items are not affected by the presence or absence of other items in the pool.
- Pasch's axiomA statement in plane geometry, used implicitly by Euclid, which cannot be derived from Euclid's postulates. It states that, if a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side.
- union axiomThe axiom stating that for every set of sets A, there exists a set C whose elements are all and only the elements of at least one B ∈ A.
- axiom schema of separationThe axiom schema stating that for every set A and every condition Sx, there exists a set B whose elements are exactly those members of A for which Sx holds.
- axiom schemeA formula in the language of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.
- axiom systemA set of axioms or axiom schemata from which theorems can be derived.
- completeness axiomThe following axiom (applied to an ordered field): for any subset of the given ordered field, if there is any upper bound for this subset, then there is also a supremum for this subset, and this supremum is an element of the given ordered …
- non-aggression axiomSynonym of non-aggression principle: The legal or political principle asserting that initiating conflict against persons or their property, or threatening to do so, is illegitimate.
- axiom schemataplural of axiom schema: A formula in the language of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.
- nonaggression axiomAlternative form of non-aggression axiom: The legal or political principle asserting that initiating conflict against persons or their property, or threatening to do so, is illegitimate.
- Playfair's axiomSynonym of parallel postulate: An axiom in Euclidean geometry: given a straight line L and a point p not on L, there exists exactly one straight line parallel to L that passes through p; a variant of this axiom, such that the number of …
- field axiomAny of the several axioms that an object should meet to be considered a mathematical field.
- axiom schema of abstractionThe axiom schema stating that for any clearly stated condition Sx, there exists a set B whose elements are exactly those objects which satisfy Sx.
- axiom schemesplural of axiom scheme: A formula in the language of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.
- axiom systemsplural of axiom system: A set of axioms or axiom schemata from which theorems can be derived.
Compound words 5
- axiomaticSelf-evident or unquestionable.
- axiomlessWithout axioms.
- axiomicRelating to axioms.
- axiomlikeResembling or characteristic of an axiom.
- axiomataplural of axiom: A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.