Definition·D003
Unordered pair
The pair {a, b} contains exactly a and b.
The singleton is
.
In words
An object x belongs to the pair of a and b exactly when x equals a or x equals b.
Rests onno axioms yet
Never needed: F02 · F03 · F04 · F05 · F06 · F08 · F09 · F10 · F11 · F12 · F13 · F14 · A01 · A02 · A03 · A04 · A05 · A06 · A07 · A08 (computed from the citation graph, not asserted).
Remarks
The unordered pair; its existence for any
is guaranteed by Pairing. The singleton
is the special case
. In Lean and Mathlib the pair is built by iterated insertion, whence the leanName Set.insert.
Used by
Propose an edit3 published revisions