Question: Let (mathscr{F}:={F subset mathbb{N}: # F

Let $\mathscr{F}:=\{F \subset \mathbb{N}: \# F<\infty\}$. Show that $\# \mathscr{F}=\# \mathbb{N}$.

[ embed $\mathscr{F}$ into $\bigcup_{k \in \mathbb{N}} \mathbb{N}^{k}$ or show that $F \mapsto \sum_{j \in F} 2^{j}$ is a bijection between $\mathscr{F}$ and $\mathbb{N}$.]

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