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Axiomatic Wiki

WDUnion of a family

Definition·D004

The union of a family of sets collects every member of a member.

In words
x belongs to the union of the family F exactly when there is some set A with A a member of the family and x a member of A.
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

The union of a collection of sets, denoted ; it exists for every family by the Union axiom (A03). The binary union is the special case , using D003.
Wikipedia ↗Set.sUnion ↗

Used by

A03D006L15L24L26L27L60T04T17T38
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