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function

vr.tr.function · thing-q11348

Let an agent handle functions by domain, codomain, rule and properties, and distinguish mathematical functions from programming functions and biological functions.

Thing Registry Cross-cutting context XCT.QLT
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

Definition Domain and rule.

Domain and codomain

Sets.

Domain

Domain and codomain.

  1. What are the domain and codomain? definition
  2. Is it defined for all inputs? boundary

Rule

How outputs are computed.

Rule

Defining rule.

  1. What rule defines it? definition
  2. Is it given by formula, table or algorithm? definition
Properties Behaviour.

Mapping properties

Injective, surjective.

Mapping

Mapping properties.

  1. Is it injective, surjective or bijective? measurement
  2. Does it have an inverse? boundary

Analytic properties

Continuity, differentiability.

Analysis

Analytic properties.

  1. Is it continuous and differentiable? measurement
  2. Where not? boundary
Representation Graphs and code.

Graph

Plot.

Graph

Graph.

  1. What does its graph look like? definition
  2. What are its key features? measurement

Computation

Evaluation.

Computation

Numerical evaluation.

  1. How can it be evaluated accurately? action
  2. Where is it numerically unstable? boundary
Use Modelling.

Model

Applications.

Model

Modelling use.

  1. What relationship does it model? definition
  2. How well does it fit data? measurement

Other senses

Programming and biology.

Senses

Disambiguation.

  1. Is the mathematical sense meant? boundary
  2. Which other entry fits better? action

Classifiers Filled

Family
Thing Registry
Category
Cross-cutting context
Entry kind
thing
Plane
XCT
Domain
XCT.QLT

What it is Filled

In mathematics, a relation that assigns to each element of a set (the domain) exactly one element of another set (the codomain).

Why it exists Filled

Let an agent handle functions by domain, codomain, rule and properties, and distinguish mathematical functions from programming functions and biological functions.

Distinguishing features Filled

  • Each input has exactly one output
  • Defined with domain and codomain
  • Partial functions leave some inputs undefined
  • Properties include injective, surjective, bijective

What robots and AI may and may not do Filled

Must not

  • Misstate a function's domain or properties in a proof or calculation.
  • Present an unverified proof as correct.
  • Claim credit for others' mathematical work.

Only with a human decision

  • Using mathematical results in safety-critical systems.

May

  • Define, compute and analyse functions.
  • Explain function concepts to learners.

Moral aspects Filled

  • Mathematical errors can propagate into critical systems.
  • Credit for results matters to mathematicians.

Who is affected

  • Students
  • Users of mathematical results

Owners Filled

Steward

Nobody owns a mathematical concept; it is held in common.

Links to other meta-models Filled

parent

  • Q130901 - registry parent class
  • Q1756942 - registry parent class

related

  • binary relation - mathematics
  • mathematics - analysis
  • function in programming or biology - other senses
  • curve - graph

What else AI and robots need to interact with it Filled

Identity and identifiers required Filled

  • Vercy registry: vr.tr.function
  • Wikidata: Q11348 (https://www.wikidata.org/wiki/Q11348)
  • DLMF chapter: NIST DLMF identifiers special functions

Direct properties not applicable Not applicable

Not applicable

Plane XCT: no invented physical properties.

Recognition optional Filled

  • Notation f: A -> B
  • Graphs passing the vertical line test
  • Programming functions are a related but different sense
  • Formulas such as f(x) = x squared, graphs and tables.

Capabilities and actions required Filled

  • define it by a rule, table or graph
  • evaluate it at points
  • study its properties such as continuity
  • compose and invert it where possible

Hazards and failure modes required Filled

  • Evaluating outside the domain
  • Confusing a function with its formula
  • Assuming invertibility

Standards and interfaces required Filled

  • ISO 80000-2 notation

Context of use required Filled

  • Describing dependence between quantities in mathematics, science and computing.
  • polynomial, rational, exponential and trigonometric functions
  • injective, surjective and bijective functions
  • partial functions
  • multivariable functions

Sources Filled

  1. Wikidata item Q11348: function - identity and sense of the item
  2. Wikipedia: Function (mathematics) - general description of the item

Open questions

  • Should classes of functions be separate entries?
  • How should programming functions be linked?
  • How should special functions be catalogued?

Machine files

Card as JSON Specification Card backlog vercy.card/1

Provenance

thing registry research (pass 2) · unreviewed

Built from: models/things/publications/thing-q11348/spec.json