Set of Infinity

Algebra Level 3

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

  1. P P does not exist.

  2. P P exist

  3. ∣ P ∣ = ℵ 0 |P| = \aleph_{0}

  4. ∣ P ∣ = ℵ 1 |P| = \aleph_{1}

  5. None of the choices

3 4 5 1 2

Paul Ryan Longhas by Paul Ryan Longhas , 24, Philippines

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1 solution

Paul Ryan Longhas
Oct 28, 2015

Note that P ∈ P P \in P , which is impossible. This is called Russell's paradox.

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