The Number Systems
E513377
The Number Systems is a mathematical work by logician Solomon Feferman that surveys and rigorously develops the hierarchy of number systems from natural numbers through real and complex numbers, emphasizing their logical foundations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| The Number Systems canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5354230 — 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: The Number Systems Context triple: [Solomon Feferman, notableWork, The Number Systems]
-
A.
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.
-
B.
Numbers
Numbers is Apple's spreadsheet application for macOS and iOS, used to create, analyze, and visualize data in tables and charts.
-
C.
Elements of Arithmetic
Elements of Arithmetic is a foundational 19th-century mathematics textbook by Augustus De Morgan that systematically develops the principles of arithmetic and number theory.
-
D.
Hindu–Arabic numeral system
The Hindu–Arabic numeral system is the globally dominant positional number system that uses ten digits (0–9) and place value to represent all integers efficiently.
-
E.
Numbers series
Numbers series is a set of iconic numeral-themed artworks by American pop artist Robert Indiana, reflecting his bold graphic style and interest in language and symbolism.
- 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: The Number Systems Target entity description: The Number Systems is a mathematical work by logician Solomon Feferman that surveys and rigorously develops the hierarchy of number systems from natural numbers through real and complex numbers, emphasizing their logical foundations.
-
A.
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.
-
B.
Numbers
Numbers is Apple's spreadsheet application for macOS and iOS, used to create, analyze, and visualize data in tables and charts.
-
C.
Elements of Arithmetic
Elements of Arithmetic is a foundational 19th-century mathematics textbook by Augustus De Morgan that systematically develops the principles of arithmetic and number theory.
-
D.
Hindu–Arabic numeral system
The Hindu–Arabic numeral system is the globally dominant positional number system that uses ten digits (0–9) and place value to represent all integers efficiently.
-
E.
Numbers series
Numbers series is a set of iconic numeral-themed artworks by American pop artist Robert Indiana, reflecting his bold graphic style and interest in language and symbolism.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
logician ⓘ mathematics book ⓘ |
| about |
Peano axioms
ⓘ
linked to:
Peano arithmetic
algebraic properties of number systems ⓘ cardinality of number systems ⓘ complete ordered fields ⓘ consistency and completeness issues in arithmetic ⓘ construction of the complex numbers ⓘ construction of the reals ⓘ formal systems for arithmetic ⓘ ordered fields ⓘ set theory and numbers ⓘ structure of the number line ⓘ |
| author | Solomon Feferman ⓘ |
| creator | Solomon Feferman ⓘ |
| field |
foundations of mathematics
ⓘ
mathematical logic ⓘ number theory ⓘ |
| focusesOn |
foundational issues in mathematics
ⓘ
logical analysis of arithmetic ⓘ rigorous development of number systems ⓘ set-theoretic construction of number systems ⓘ |
| genre |
mathematics textbook
ⓘ
monograph ⓘ |
| hasPart |
development of the complex numbers
ⓘ
development of the integers ⓘ development of the natural numbers ⓘ development of the rational numbers ⓘ development of the real numbers ⓘ discussion of axioms for arithmetic ⓘ discussion of logical foundations of number systems ⓘ discussion of set-theoretic constructions ⓘ |
| intendedAudience |
advanced undergraduates in mathematics
ⓘ
graduate students in mathematics ⓘ researchers in logic and foundations ⓘ |
| language | English ⓘ |
| mainSubject |
axiomatic development of number systems
ⓘ
complex numbers ⓘ hierarchy of number systems ⓘ integers ⓘ logical foundations of arithmetic ⓘ natural numbers ⓘ number systems ⓘ rational numbers ⓘ real numbers ⓘ |
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: The Number Systems Description of subject: The Number Systems is a mathematical work by logician Solomon Feferman that surveys and rigorously develops the hierarchy of number systems from natural numbers through real and complex numbers, emphasizing their logical foundations.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.