real-valued function
Let an agent define real-valued functions, relay their main properties and classes from analysis references, describe applications in optimisation and approximation, and distinguish them from complex-valued and vector-valued functions.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Define Definition.
Definition
Definition.
Definition
Definition.
- What is a real-valued function, and how does the domain vary? definition
- Is the function real-valued, complex-valued or vector-valued? boundary
Properties
Properties.
Properties
Properties.
- What are continuity, differentiability, integrability, monotonicity and convexity? definition
- Which entry fits the specific property? action
Classes Special classes.
Optimisation
Convex and quasiconvex.
Optimisation
Optimisation.
- What are convex and quasiconvex functions, and why do they matter in optimisation? provenance
- Which entry fits quasiconvex function? action
Other
Radial basis and quasimorphisms.
Other
Other.
- What are radial basis functions and quasimorphisms, and where are they used? provenance
- Which references are standard? provenance
Apply Applications.
Modelling
Modelling.
Modelling
Modelling.
- How are real-valued functions used to model quantities in science and economics? provenance
- Which sources are cited? provenance
Approximation
Approximation and computation.
Approximation
Approximation.
- How are real functions approximated and computed numerically? provenance
- Which entry fits numerical analysis? action
Context Foundations and history.
Foundations
Foundations.
Foundations
Foundations.
- How does the construction of the real numbers underpin real-valued functions? provenance
- Which entry fits real number? action
History
History.
History
History.
- How did the modern function concept develop from Euler to Dirichlet and Weierstrass? provenance
- Which entry fits the history of analysis? action
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- real-valued function on a real interval, real-valued function of a real variable, quasimorphism, quasiconvex function, harmonic index of a graph, radial basis function, integer-valued function, pseudo-absolute value, power curve, Entanglement measure, Lorentzian function, atomic function
What it is Filled
A function whose values are real numbers, most commonly a real-valued function of a real variable defined on an interval or subset of the real line, the central object of calculus and real analysis, but also functions from other domains to the reals such as quasimorphisms on groups, quasiconvex functions in optimisation, radial basis functions in approximation and graph invariants such as the harmonic index; real-valued functions are studied for continuity, differentiability, integrability and convexity.
Why it exists Filled
Let an agent define real-valued functions, relay their main properties and classes from analysis references, describe applications in optimisation and approximation, and distinguish them from complex-valued and vector-valued functions.
Distinguishing features Filled
- Real codomain
- Order structure of values
- Calculus properties
- Many special classes
What robots and AI may and may not do Filled
Must not
- Claim properties of a function, such as continuity or boundedness, without proof or check.
- Report results from floating point evaluation as exact real values without noting rounding.
- Present copied proofs or solutions as a student's own work for graded assessment.
Only with a human decision
- Using a model function to make decisions that affect people, such as pricing or risk scores.
May
- Define, evaluate, plot and analyze real-valued functions.
- Check domains, continuity and limits in calculations it is asked to verify.
Moral aspects Filled
- Functions used in models can encode unfair assumptions that look neutral because they are mathematical.
- Academic honesty depends on agents not doing graded work for students.
Who is affected
- Students and teachers
- People scored by mathematical models
Owners Filled
Steward
Nobody owns the concept; it belongs to shared mathematical knowledge.
Links to other meta-models Filled
parent
- Q11893837 - registry parent class
related
- scalar function - in registry terms
- real analysis - the field
- complex-valued function - with complex codomain
- continuous function - as a major class
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.real-valued-function
- Wikidata: Q5189500 (https://www.wikidata.org/wiki/Q5189500)
Direct properties not applicable Not applicable
Not applicable
Plane XCT: no invented physical properties.
Recognition optional Filled
- Function with real number values
- Functions of a real variable, quasiconvex, radial basis, quasimorphisms
- Complex-valued and vector-valued functions have other codomains
- A graph in the plane for functions of one real variable.
Capabilities and actions required Filled
- define and classify
- relay properties
- describe applications
- distinguish from other function types
Hazards and failure modes required Filled
- Confusing domain and codomain conditions
- Assuming continuity or differentiability
- Conflating unrelated special classes
Standards and interfaces required Filled
- No regulation; mathematical conventions
Context of use required Filled
- Not applicable; a mathematical object.
- real-valued functions of a real variable on intervals
- continuous, differentiable and integrable functions
- convex and quasiconvex functions
- radial basis functions
- quasimorphisms on groups
- real-valued graph invariants such as the harmonic index
- real-valued functions on measure spaces
Sources Filled
- Wikidata item Q5189500: real-valued function - identity and sense of the item
- Wikipedia: Real-valued function - general description of the item
Open questions
- Should function of a real variable be the primary linked entry?
- How should analysis references be linked?
- The registry entry has merged aliases naming unrelated special classes; should they be split off?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q5189500/spec.json