Infinite countable union of finite sets

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If $A_n$ is finite $\forall n\in \mathbb N,\;$ then countable infinite union of these sets is infinite, right?

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1 Answer

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Wrong. Take for example $$ \forall n\in \Bbb N : A_n = \{1\} $$ Every $A_n$ is finite (having just one element!) and the infinite union of all $A_n$ is still finite.

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