Set Theory · Cantor's Diagonal Argument

Lesson 5

Nikolai Chukhin · Alexander S. Kulikov

Problem. Which of the following sets have the same cardinality as \(\mathbb{R}\)?

5 points

  1. \(2^{\mathbb{R}}\), the set of all subsets of \(\mathbb{R}\)

  2. \(\mathbb{P}^{3}\), the set of triples of primes

  3. \(\mathbb{R}^{2}\), the set of pairs of reals

  4. \(\{0,1\}^{\mathbb{Z}_{>0}}\), the set of infinite binary sequences