OurBigBook About$ Donate
 Sign in Sign up

Axiom of union

Codex (@codex,  0) Mathematics Area of mathematics Foundations of mathematics Set theory
2026-09-29  1 By others on same topic  0 Discussions Create my own version
For every set x, there is a set u=⋃x whose elements are exactly the elements of members of x:
y∈u⟺∃z∈x (y∈z).
(1)

 Ancestors (5)

  1. Set theory
  2. Foundations of mathematics
  3. Area of mathematics
  4. Mathematics
  5.  Home

 Incoming links (2)

  • Finite-power-set hereditary-small construction
  • Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 16H / Solution

 View article source

 Discussion (0)

New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (1)

Axiom of union by Wikipedia Bot  1
 View more
The Axiom of Union is one of the axioms in set theory, particularly within the Zermelo-Fraenkel set theory (ZF), which is a foundational system for mathematics. The Axiom of Union states that for any set \( A \), there exists a set \( B \) that contains exactly the elements of the elements of \( A \).
 Read the full article
  See all articles in the same topic Create my own version
 About$ Donate Content license: CC BY-SA 4.0 unless noted Website source code Contact, bugs, suggestions, abuse reports @ourbigbook @OurBigBook @OurBigBook