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There are infinite non-equipotent infinite sets

The sets

$$\mathbb{N}$$ $$\mathcal{P}(\mathbb{N})$$ $$\mathcal{P}(\mathcal{P}(\mathbb{N}))$$ $$\mathcal{P}(\mathcal{P}(\mathcal{P}(\mathbb{N})))$$ $$\mathcal{P}(\mathcal{P}(\mathcal{P}(\mathcal{P}(\mathbb{N}))))$$ $$...$$

are all infinite, and each one is strictly bigger than the previous one