function
Let an agent handle functions by domain, codomain, rule and properties, and distinguish mathematical functions from programming functions and biological functions.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent handle functions by domain, codomain, rule and properties, and distinguish mathematical functions from programming functions and biological functions.
In mathematics, a relation that assigns to each element of a set (the domain) exactly one element of another set (the codomain).
What it is for: Describing dependence between quantities in mathematics, science and computing.
It can be define it by a rule, table or graph; evaluate it at points; study its properties such as continuity; compose and invert it where possible.
Distinguishing features
Each input has exactly one output
Defined with domain and codomain
Partial functions leave some inputs undefined
Properties include injective, surjective, bijective
What it looks like
Formulas such as f(x) = x squared, graphs and tables.
How it is recognised
Notation f: A -> B
Graphs passing the vertical line test
Programming functions are a related but different sense
Related models
is a kind of - mathematics
is studied by - analysis
is confused with - other senses
is represented by - graph
In practice
Families and kinds
polynomial, rational, exponential and trigonometric functions
injective, surjective and bijective functions
partial functions
multivariable functions
Identifiers
DLMF chapter NIST DLMF identifiers special functions
Standards and regulation
ISO 80000-2 notation
Failure modes and hazards
Evaluating outside the domain
Confusing a function with its formula
Assuming invertibility
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.function-group
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Definition Domain and rule.
Domain and rule define a function.
Domain and codomain
Sets.
Domain
Domain and codomain.
- What are the domain and codomain? definition
- Is it defined for all inputs? boundary
Rule
How outputs are computed.
Rule
Defining rule.
- What rule defines it? definition
- Is it given by formula, table or algorithm? definition
Properties Behaviour.
Properties decide what can be done.
Mapping properties
Injective, surjective.
Mapping
Mapping properties.
- Is it injective, surjective or bijective? measurement
- Does it have an inverse? boundary
Analytic properties
Continuity, differentiability.
Analysis
Analytic properties.
- Is it continuous and differentiable? measurement
- Where not? boundary
Representation Graphs and code.
Representations help use.
Graph
Plot.
Graph
Graph.
- What does its graph look like? definition
- What are its key features? measurement
Computation
Evaluation.
Computation
Numerical evaluation.
- How can it be evaluated accurately? action
- Where is it numerically unstable? boundary
Use Modelling.
Functions model relationships.
Model
Applications.
Model
Modelling use.
- What relationship does it model? definition
- How well does it fit data? measurement
Other senses
Programming and biology.
Senses
Disambiguation.
- Is the mathematical sense meant? boundary
- Which other entry fits better? action
What the second pass must settle
- Should classes of functions be separate entries?
- How should programming functions be linked?
- How should special functions be catalogued?