TITLE: Can any infinite set be written as the union of finite sets?
QUESTION [13 upvotes]: While working on a problem, I was wondering about the following: Is it  possible to write any infinite set as union of finite sets or not ?

REPLY [31 votes]: Sure, it's possible. Let $X$ be any set. Then
$$
X = \bigcup_{x \in X} \{x \}.
$$
So any set is a union of singletons (except maybe for the empty set - dependent on how you'd interpret the above formula in this case).