Published
integer
vr.tr.integer · thing-q12503
Let an agent reason about integers mathematically and in computing, where fixed-width representations add overflow and signedness issues.
Thing Registry Cross-cutting context XCT.QTY
Bundle → Layer → Finding → QuestionsClassifiersWhat it isWhy it existsDistinguishing featuresWhat robots and AI may and may not doMoral aspectsOwnersLinks to other meta-modelsIdentity and identifiersDirect propertiesRecognitionCapabilities and actionsHazards and failure modesStandards and interfacesContext of useSources
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Mathematics Properties of integers.
Arithmetic
Operations and closure.
Operations
Operations and results.
- Does the operation stay within the integers? definition
- How is division with remainder defined here for negatives? boundary
Properties
Parity, primality, divisibility.
Properties
Number-theoretic properties.
- Is it even or odd, prime or composite? measurement
- What are its divisors? measurement
Representation In computers.
Width and sign
int32, int64, unsigned.
Type
The type and range.
- Which integer type holds this value, and what is its range? definition
- Is it signed or unsigned? definition
Overflow
Wraparound and errors.
Overflow handling
How overflow is handled.
- Can this calculation overflow? boundary
- Is overflow checked, wrapped or saturated? definition
Interchange Passing integers between systems.
Formats
JSON, CSV, databases.
Format limits
Limits of formats.
- Will this integer survive the format without loss? boundary
- Should it be sent as a string? action
Parsing
Leading zeros and separators.
Parsing rules
Parsing rules.
- How are leading zeros and separators handled? boundary
- Is the value an identifier rather than a number? definition
Identifiers Integers as labels.
Label or quantity
Nature of the value.
Nature
Whether the integer is a label.
- Is this integer a quantity or a label? definition
- What operations make sense on it? boundary
Uniqueness
Scope of identifiers.
Scope
Where the identifier is unique.
- Within what scope is this identifier unique? boundary
- Can it be reused? boundary
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QTY
- Other names and narrower kinds
- process identifier, even house number, odd house number, logical block address, intersection number, non-negative integer, order of reflexion, Miller index, Skewes' number, minimum vertex degree, sphericity, Takeuchi number
What it is Filled
A number that is zero, a positive whole number or the negative of one: ..., -2, -1, 0, 1, 2, ...; the set Z.
Why it exists Filled
Let an agent reason about integers mathematically and in computing, where fixed-width representations add overflow and signedness issues.
Distinguishing features Filled
- Whole numbers, positive, negative and zero
- Closed under addition, subtraction and multiplication, not division
- Computer integers have fixed ranges unless arbitrary precision
- Numeric identifiers are not quantities
What robots and AI may and may not do Filled
Must not
- Let integers silently overflow or wrap in calculations that matter.
- Mix signed and unsigned integers without checking.
- Do arithmetic on identifiers that only look like numbers.
Only with a human decision
- Changing integer types in systems that hold money or safety values.
May
- Perform integer arithmetic within stated bounds and check for overflow.
- Store large integers, such as identifiers, as strings where floating point would round them.
Moral aspects Filled
- Integer errors have caused failures in finance, aviation and medicine.
Who is affected
- Users of software
- People whose records are counted
Owners Filled
Steward
Nobody owns the integers; they are held in common.
Links to other meta-models Filled
parent
- Q11756524 - registry parent class
- Q724975 - registry parent class
- Q8424307 - registry parent class
related
- number - the set Z
- sign - positive, negative or zero
- identifier - numeric labels
- floating-point number - approximate reals
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.integer
- Wikidata: Q12503 (https://www.wikidata.org/wiki/Q12503)
- OEIS: A-numbers integer sequences
Direct properties not applicable Not applicable
- int32 range: -2147483648 to 2147483647 dimensionless
- int64 maximum: 9223372036854775807 dimensionless
Plane XCT: no invented physical properties.
Recognition optional Filled
- Numerals with no decimal point
- Types such as int32, int64, BigInt in code
- Identifiers that look like integers are labels, not quantities
- Digits without a fractional part, optionally with a minus sign.
Capabilities and actions required Filled
- add, subtract and multiply, staying within the integers
- divide with remainder
- store it, in fixed or arbitrary precision
- use it as an identifier, such as a process id or block address
Hazards and failure modes required Filled
- Integer overflow and wraparound
- Signed and unsigned mismatches
- Rounding when integers pass through floating point, such as in JSON beyond 2^53
- Doing arithmetic on identifiers
Standards and interfaces required Filled
- ISO 80000-2 notation
- ISO/IEC 9899 C and other language standards defining integer types
Context of use required Filled
- Counting, indexing, identifiers and exact arithmetic.
- natural numbers and non-negative integers
- even and odd integers
- primes
- signed and unsigned machine integers
Sources Filled
- Wikidata item Q12503: integer - identity and sense of the item
- Wikipedia: Integer - general description of the item
Open questions
- Should machine integer types be separate entries?
- How should identifiers be marked so they are not treated as quantities?
- The registry entry has merged aliases such as house numbers; should they be split off?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q12503/spec.json