For example $\bigcup_{n\in \mathbb{N}}A_n=\mathbb{N}$
My proof, to prove that two sets are equal i must show that they are subsets of each other. I understand how to show $\bigcup_{n\in \mathbb{N}}A_n\subseteq\mathbb{N}$ but i get stuck with with the other way to show that $\mathbb{N}\subseteq\bigcup_{n\in \mathbb{N}}A_n$
My proof for that is, given an element $x\in\mathbb{N}$ since $A_x\subseteq\mathbb{N}$ then $x\in A_x$ and means that $x\in\bigcup_{n\in \mathbb{N}}A_n$ for some $n\in\mathbb{N}$
please help, thanks in advance.