Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-generatedSession-authored (Fable 5 assisted)precheck passaudited 2026-08-27
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

FALSE: Bell numbers count ordered set partitions

Statement

False claim: the Bell number Bn counts ordered set partitions of [n].

Facts & Assumptions

Given: The Bell numbers and ordered Bell numbers already discussed on this page.

Proof

technique · direct
1.1

For n=3, The Stirling numbers of the second kind and the Bell numbers gives B3=5.

given
2.1

But the ordered set partitions of [3] are counted by 1⋅1!+3⋅2!+1⋅3!=13. Since 5≠13, the Bell numbers do not count ordered set partitions.

step 1.1givenalgebra
3.1

Therefore the claim is false.

step 2.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

7 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources