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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