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Canonical static concept record

Limit ordinal

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Summary

A nonzero ordinal that is not a successor ordinal; equivalently, an ordinal equal to the union of all smaller ordinals.

Record metadata

Canonical name: Limit ordinal
Concept ID: limit_ordinal
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: Ordinal class

Carrier(s)

ordinal $\lambda$

Axioms / constraints

$\lambda\ne0$ and $\alpha+1<\lambda$ for every $\alpha<\lambda$

Canonically induces

limit stages of transfinite definitions

Notes

$\omega$ is the first limit ordinal.

Concept sources

Wikipedia — Ordinal number — Ordinal number · expository · source ID wp-ordinal
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.

Ordinal Limit ordinal

Permalink to relation

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

Relation ID: ordinal_to_limit_ordinal
Relation type: Classification classification
Direction: source → target
Endpoint roles: source: Has subtype; target: Classified as
Authored annotation: limit ordinals

Authored explanation

Limit ordinals are the nonzero ordinals with no immediate predecessor.

How to interpret this relation type

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

Relation sources

Wikipedia — Ordinal number — Ordinal number · expository · source ID wp-ordinal
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.

Limit ordinal First infinite ordinal $\omega$

Permalink to relation

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

Relation ID: limit_ordinal_to_omega
Relation type: Classification classification
Direction: source → target
Endpoint roles: source: Has subtype; target: Classified as
Authored annotation: first limit ordinal

Authored explanation

$\omega$ is the least nonzero limit ordinal.

How to interpret this relation type

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

Relation sources

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

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Limit ordinal

Summary

Record metadata

Carrier(s)

Axioms / constraints

Canonically induces

Notes

Concept sources

Incoming relations (arrows to this concept)

Ordinal Limit ordinal

Authored explanation

How to interpret this relation type

Relation sources

Outgoing relations (arrows from this concept)

Limit ordinal First infinite ordinal $\omega$

Authored explanation

How to interpret this relation type

Relation sources