Conway chained arrow notation
E163257
Conway chained arrow notation is a mathematical system of hyper-operator-style notation introduced by John Horton Conway to concisely represent extremely large numbers.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Conway chained arrow notation canonical | 4 |
How this entity was disambiguated
This entity first appeared as the object of triple T1428687 — 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: Conway chained arrow notation Context triple: [John Horton Conway, notableWork, Conway chained arrow notation]
-
A.
Knuth’s up-arrow notation
Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
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B.
Peano notation
Peano notation is a formal symbolic system for representing natural numbers and arithmetic operations using axioms and successor functions, developed by Giuseppe Peano.
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C.
Surreal numbers
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.
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D.
Look-and-say sequence
The look-and-say sequence is a famous integer sequence where each term is generated by verbally describing the digits of the previous term, studied for its surprising combinatorial and growth properties.
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E.
Gödel numbering
Gödel numbering is a method in mathematical logic that encodes symbols, formulas, and proofs as unique natural numbers, enabling arithmetic to represent and reason about syntactic statements.
- 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: Conway chained arrow notation Target entity description: Conway chained arrow notation is a mathematical system of hyper-operator-style notation introduced by John Horton Conway to concisely represent extremely large numbers.
-
A.
Knuth’s up-arrow notation
Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
-
B.
Peano notation
Peano notation is a formal symbolic system for representing natural numbers and arithmetic operations using axioms and successor functions, developed by Giuseppe Peano.
-
C.
Surreal numbers
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.
-
D.
Look-and-say sequence
The look-and-say sequence is a famous integer sequence where each term is generated by verbally describing the digits of the previous term, studied for its surprising combinatorial and growth properties.
-
E.
Gödel numbering
Gödel numbering is a method in mathematical logic that encodes symbols, formulas, and proofs as unique natural numbers, enabling arithmetic to represent and reason about syntactic statements.
- F. None of above. chosen
Statements (38)
| Predicate | Object |
|---|---|
| instanceOf |
hyperoperation-style notation
ⓘ
large-number notation ⓘ mathematical notation ⓘ |
| appearsInWorkOf |
John H. Conway
ⓘ
surface form:
John Horton Conway
other large-number theorists ⓘ |
| category | notation for fast-growing functions ⓘ |
| comparedWith | Knuth up-arrow notation for expressive power ⓘ |
| complexity | non-elementary growth ⓘ |
| creator |
John H. Conway
ⓘ
surface form:
John Horton Conway
|
| domainRestriction | usually defined for positive integers ⓘ |
| enablesDefinitionOf | numbers larger than those expressible by Knuth up-arrows of fixed height ⓘ |
| expressivePower | can represent numbers far beyond primitive recursive functions ⓘ |
| field |
combinatorics
ⓘ
large numbers ⓘ mathematics ⓘ number theory ⓘ |
| generalizes |
iterated exponentiation
ⓘ
power towers ⓘ |
| growthRate | extremely fast-growing ⓘ |
| hasComponent | finite chain of positive integers separated by arrows ⓘ |
| hasNameOrigin | named after John Horton Conway ⓘ |
| hasProperty |
not commonly used in mainstream analysis
ⓘ
primarily of theoretical and recreational interest ⓘ |
| introducedBy |
John H. Conway
ⓘ
surface form:
John Horton Conway
|
| mathematicalObjectType | partial function on tuples of integers ⓘ |
| notationForm | chained arrow notation ⓘ |
| notationType | infix notation ⓘ |
| purpose | to concisely represent extremely large numbers ⓘ |
| relatedTo |
Ackermann-type functions
ⓘ
Knuth’s up-arrow notation ⓘ
surface form:
Knuth up-arrow notation
hyperoperations ⓘ tetration ⓘ |
| representationStyle | finite symbolic expressions for enormous integers ⓘ |
| typicalUse |
illustrating hierarchies of large numbers
ⓘ
theoretical analysis of very large numbers ⓘ |
| usedIn |
large-number contests and examples
ⓘ
recreational mathematics ⓘ |
| usesSymbol | → ⓘ |
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: Conway chained arrow notation Description of subject: Conway chained arrow notation is a mathematical system of hyper-operator-style notation introduced by John Horton Conway to concisely represent extremely large numbers.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
John Horton Conway
subject surface form:
John H. Conway