Definition·D006
Von Neumann successor
The successor of x is x union {x}.
In words
The successor of x is x itself together with the singleton containing x.
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
Von Neumann successor. Together with D002 it builds the finite ordinals
,
,
, and so on, which are gathered into the set of natural numbers, and underlies the infinity axiom A05.
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