1.11 Infinite Sets

Cantor's Diagonal Argument


  1. The Diagonal Argument was used to illustrate that the set of infinite binary sequences, \(\{ 0, 1 \} ^ \omega \), is _____,

    Exercise 1

    by building a _____

    Exercise 2

    that is _____ the list of infinite binary sequences.

    Exercise 3
  2. The set of natural numbers is strictly smaller than the set, \(A \), of infinite binary strings (i.e. \(\mathbb{N} \) strict \(A \)), because _____.

    Exercise 4
  3. Cantor's Theorem states that for any set \(A \), finite or infinite, _____ pow(\(A \)).

    Exercise 5