Set of Infinity

Algebra Level 3

Let $$P =$${$$S_{1}, S_{2}, S_{3},....$$} be a set provided that $$\forall i \in \mathbb{N}, S_{i} \in P$$ is a set whose number of elements is infinitely many [example: $$\mathbb{R} \in P$$]. Which of the following is true?

1. $$P$$ does not exist.

2. $$P$$ exist

3. $$|P| = \aleph_{0}$$

4. $$|P| = \aleph_{1}$$

5. None of the choices

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