Can any infinite set be written as the union of finite sets?

elementary-set-theory

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 ?


Solution 1:

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).

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