Surreal numbers
E29943
Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
All labels observed (6)
| Label | Occurrences |
|---|---|
| Surreal numbers canonical | 3 |
| Conway normal form | 1 |
| Conway numbers | 1 |
| Conway surreal numbers | 1 |
| Surreal Numbers | 1 |
| surreal numbers | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T231139 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Surreal numbers Context triple: [John H. Conway, notableWork, Surreal numbers]
-
A.
von Neumann paradox in set theory
The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
-
B.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
C.
Conway’s Game of Sprouts
Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
-
D.
von Neumann universe
The von Neumann universe is a cumulative, well-founded hierarchy of sets used as a standard model of the set-theoretic universe in axiomatic set theory.
-
E.
Numbers
Numbers is the fourth book of the Hebrew Bible and the Christian Old Testament, recounting the Israelites’ wilderness wanderings and organizing laws and censuses.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Surreal numbers Target entity description: Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
-
A.
von Neumann paradox in set theory
The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
-
B.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
C.
Conway’s Game of Sprouts
Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
-
D.
von Neumann universe
The von Neumann universe is a cumulative, well-founded hierarchy of sets used as a standard model of the set-theoretic universe in axiomatic set theory.
-
E.
Numbers
Numbers is the fourth book of the Hebrew Bible and the Christian Old Testament, recounting the Israelites’ wilderness wanderings and organizing laws and censuses.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
Conway number
ⓘ
number system ⓘ ordered field ⓘ proper class ⓘ |
| alternativeName |
Surreal numbers
ⓘ
surface form:
Conway numbers
|
| birthProcess | numbers are created in stages indexed by ordinals ⓘ |
| constructedFrom | left set and right set of earlier numbers ⓘ |
| containsAsSubfield |
ordinal numbers
ⓘ
real numbers ⓘ |
| containsElement |
-1
ⓘ
0 ⓘ 1 ⓘ 1/ω (a positive infinitesimal) ⓘ all dyadic rationals ⓘ all ordinal numbers ⓘ all real numbers ⓘ ω (first infinite ordinal as a number) ⓘ |
| definedBy | transfinite recursion ⓘ |
| extends |
ordered fields
ⓘ
real numbers ⓘ |
| generalizes | Dedekind-complete ordered fields ⓘ |
| hasCanonicalForm |
Surreal numbers
self-linksurface differs
ⓘ
surface form:
Conway normal form
|
| hasOrderType | proper class length ⓘ |
| hasProperty |
every set of surreals has a greatest lower bound
ⓘ
every set of surreals has a least upper bound ⓘ no maximal element ⓘ no minimal element other than zero ⓘ real-closed field ⓘ totally ordered ⓘ |
| hasSubset | day-n numbers (numbers born on day n in the construction) ⓘ |
| includes |
infinite numbers
ⓘ
infinitesimal numbers ⓘ |
| introducedBy |
John H. Conway
ⓘ
surface form:
John Horton Conway
|
| introducedInPublication | On Numbers and Games ⓘ |
| introducedInYear | 1974 ⓘ |
| isClassOf | all numbers generated from the empty set by Conway’s rules ⓘ |
| isModelOf |
ordered field axioms
ⓘ
real-closed field axioms ⓘ |
| relatedConcept |
Hahn series
ⓘ
hyperreal numbers ⓘ nonstandard analysis ⓘ |
| satisfiesCondition | every left element is less than every right element ⓘ |
| supportsOperation |
addition
ⓘ
division ⓘ exponentiation (partial) ⓘ multiplication ⓘ subtraction ⓘ |
| usedIn | combinatorial game theory ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Surreal numbers Description of subject: Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Surreal Numbers
this entity surface form:
Conway numbers
this entity surface form:
Conway normal form
subject surface form:
John Horton Conway
this entity surface form:
surreal numbers
subject surface form:
John H. Conway
this entity surface form:
Conway surreal numbers