Lecture 19 Level 2/4 Error in Description

[KellyJDavis]

The text

For example, if σ sends 0 → 1000000, we might have to wait a while, but eventually (before reaching some N), all of {0, 1, ..., M} will have appeared as values σ(k) for k < N.

is phrased slightly incorrectly. It should read

For example, if σ sends 0 → 1000000, we might have to wait a while, but eventually (before reaching some N), all of {0, 1, ..., M-1} will have appeared as values σ(k) for k < N.

The set {0, 1, ..., M} should be {0, 1, ..., M-1} as the conclusion of the theorem is

∃ N, ∀ n ≥ N, (range M) ⊆ image σ (range n)

note (range M) ⊆ image σ (range n) and not (range (M + 1)) ⊆ image σ (range n) appears in conclusion.