# 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