In Theorem 3.21, we showed that a language is Turing-recognizable iff some enumerator enumerates it. Why didn’t we use the following simpler algorithm for the forward direction of the proof? As before, s₁, s₂, . . . is a list of all strings in Σ^*.

E = “Ignore the input.

1. Repeat the following for i = 1, 2, 3, . . . .

2. RunM on s_i.

3. If it accepts, print out s_i.”