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Construction junctions are diamonds. They show where multiple structures must coexist on the same carrier and satisfy compatibility conditions.

Canonical static concept record

Finite set

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Summary

A set in bijection with $\{0,\ldots,n-1\}$ for some natural number $n \in \mathbb{N}$ , including $n=0$ .

Record metadata

Canonical name: Finite set
Concept ID: finite_set
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Set theory
Domains: Set theory, Combinatorics & graph theory
Alternate terminology: No alternate terminology is currently authored for this record.

Carrier(s)

set $X$

Axioms / constraints

finite cardinality

Concept sources

Wikipedia — Finite set — Finite set · expository · source ID wp-finite-set
nLab — Finite set — Finite set · mathematical reference · source ID nlab-finite-set
Open Logic Project — Set Theory — Open Logic Project: Set Theory · open textbook source · source ID openlogic-set-theory

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Set Finite set

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: e_set_finite
Relation type: Impose axiom impose-axiom
Direction: source → target
Endpoint roles: source: Builds toward; target: Built from
Authored annotation: + finite cardinality

Authored explanation

Restrict to sets with finitely many elements.

How to interpret this relation type

Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.

Relation sources

Wikipedia — Finite set — Finite set · expository · source ID wp-finite-set
Open Logic Project — Set Theory — Open Logic Project: Set Theory · open textbook source · source ID openlogic-set-theory

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Finite set Finite ordinal

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: finite_set_to_finite_ordinal
Relation type: Impose axiom impose-axiom
Direction: source → target
Endpoint roles: source: Builds toward; target: Built from
Authored annotation: require ordinal form

Authored explanation

Select the finite sets that are transitive and well-ordered by membership; these are the finite von Neumann ordinals.

How to interpret this relation type

Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.

Relation sources

Wikipedia — Von Neumann ordinal — Von Neumann ordinal · encyclopedic reference · source ID wp-von-neumann-ordinal
Open Logic Project — Set Theory — Open Logic Project: Set Theory · open textbook source · source ID openlogic-set-theory

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Finite set

Summary

Record metadata

Carrier(s)

Axioms / constraints

Concept sources

Incoming relations (arrows to this concept)

Set Finite set

Authored explanation

How to interpret this relation type

Relation sources

Outgoing relations (arrows from this concept)

Finite set Finite ordinal

Authored explanation

How to interpret this relation type

Relation sources