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WDVon Neumann successor

Definition·D006

The successor of x is x union {x}.

combining the binary union of D004 with the singleton of D003.
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 · A09 (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.
Wikipedia ↗SuccOrder.succ ↗

Used by

A05D025D026D027D119L04L06L07L15L24L25L27L60T05T06T12T20
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