Theorem

Konig's Lemma

Logic and Foundations

Konig's Lemma states that every infinite tree in which each node has only finitely many children, and which has nodes at every finite depth, must contain an infinite path. Named for Denes Konig, it is a basic combinatorial principle used throughout logic and computability theory, notably in compactness-style arguments.

Facts

Statement

Every connected, locally finite, infinite graph contains a ray: a simple path starting at one vertex that continues through infinitely many vertices without repeating any. 1

Proof Year

1927 1

Classification

Statement Form

Existence Theorem 1

Connections

Has Statement Form

Existence Theorem

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Logic and Foundations

Sources

1. Konig's Lemma (Wikipedia)

Wikimedia Foundation

Statement of the lemma section, plain-English aside
Another way of stating the theorem is: "If the human race never dies out, somebody now living has a line of descendants that will never die out".
Lead paragraph, first sentence
Konig's lemma or Konig's infinity lemma is a theorem in graph theory due to the Hungarian mathematician Denes Konig who published it in 1927.

Switch Atlas

The Inner World

The Civil World

The Natural World

Konig's Lemma

Has Statement Form

In Branch