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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

Infinite cardinal

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Summary

A cardinal that is not finite.

Record metadata

Canonical name: Infinite cardinal
Concept ID: infinite_cardinal
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Set theory
Domains: Set theory, Order theory, Logic
Alternate terminology: No alternate terminology is currently authored for this record.
Concept type: Cardinal class

Carrier(s)

initial ordinal $\kappa$

Axioms / constraints

$\kappa\ge\aleph_0$

Notes

There is no greatest infinite cardinal, by Cantor’s theorem.

Concept sources

Wikipedia — Cardinal number — Cardinal number · expository · source ID wp-cardinal
nLab — Infinite cardinal — Infinite cardinal · mathematical reference · source ID nlab-infinite-cardinal
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.

Cardinal Infinite cardinal

Permalink to relation

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

Relation ID: cardinal_to_infinite_cardinal
Relation type: Classification classification
Direction: source → target
Endpoint roles: source: Has subtype; target: Classified as
Authored annotation: infinite cardinals

Authored explanation

Infinite cardinals are the nonfinite initial ordinals.

How to interpret this relation type

The target is a member or subtype of the broader source class.

Relation sources

Wikipedia — Cardinal number — Cardinal number · expository · source ID wp-cardinal
Open Logic Project — Set Theory — Open Logic Project: Set Theory · open textbook source · source ID openlogic-set-theory

Outgoing relations (arrows from this concept)

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