function
(mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)
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, separate from function in the sense of purpose or social event.
In mathematics, a relation that assigns to each element of a domain exactly one element of a codomain, such as polynomials, trigonometric functions and mappings between sets.
What it is for: Describing dependencies between quantities across mathematics, science and computing.
It can be evaluate it; plot it; analyse properties such as continuity; compose and invert functions.
Distinguishing features
Each input has exactly one output
Domain and codomain are part of the definition
Properties: injective, surjective, continuous
Programming functions are related but different
What it looks like
Formulas, graphs, tables or mappings.
How it is recognised
Notation f(x) or f: A -> B
Graphs passing the vertical line test
Polynomials are a family of functions
Related models
is a kind of - category
includes - family
is expanded as - representation
is confused with - another sense
In practice
Families and kinds
polynomial functions
rational functions
exponential and logarithmic functions
trigonometric functions
functions of several variables
Standards and regulation
ISO 80000-2 notation
Failure modes and hazards
Ignoring domain restrictions
Confusing senses
Analytical facets
- substance
- abstract
- origin
- conceptual
- agency
- inert
- mobility
- not-applicable
- scale
- not-applicable
- affordances
- observable
Also called
+34
Where this came from
oewn:2024 · CC BY 4.0
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 Which function.
Domain and rule define it.
Rule
Formula or mapping.
Rule
Rule.
- What rule defines the function? definition
- Is it well-defined? boundary
Domain
Inputs and outputs.
Domain
Domain and codomain.
- What are its domain and codomain? definition
- What is its range? measurement
Properties Behaviour.
Properties describe behaviour.
Mapping
Injective, surjective.
Mapping
Mapping properties.
- Is it injective, surjective or bijective? boundary
- Does it have an inverse? boundary
Analysis
Continuity.
Analysis
Analytic properties.
- Is it continuous or differentiable? boundary
- Where are its zeros and extrema? measurement
Representation Forms.
Functions have many forms.
Graph
Plot.
Graph
Graph.
- What does its graph look like? definition
- Which features should be shown? action
Series
Expansions.
Series
Series.
- Can it be written as a series? definition
- Where does it converge? boundary
Senses Disambiguation.
Function has many senses.
Other senses
Purpose, event.
Senses
Other senses.
- Is purpose, a social function or a programming function meant? boundary
- Which entry fits? action
Teaching
Explaining.
Teaching
Teaching.
- How can functions be explained clearly? action
- What misconceptions are common? boundary
What the second pass must settle
- Should function families be separate entries?
- How should programming functions be linked?
- The registry aliases list polynomial types; should they link to a polynomial entry?