Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Given an infinite set of sets A - how can I prove in ZFC that the union of all the elements of A exists?

share|cite|improve this question
See Wikipedia: Axiom of union. – Martin Sleziak Aug 6 '12 at 9:57
up vote 6 down vote accepted

It is the axiom of union which assert this.

The axiom states that if $A$ is a set, then there exists a set $B$ such that $B=\bigcup A$, that is to say

For every $x$, $x\in B$ if and only if there exists $y$ such that $y\in A$ and $x\in y$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.