Where is the flaw in the following proof, that if a language is Turing recognizable then we can enumerate it?
Let $TM1$ be a Turing machine for language $L$.
We can create an enumerator $E$ for $L$ as follows:
Repeat the following for $i = 1, 2, 3, \dots$
Run $TM1$ on $S_i$
If accepted, print out $S_i$
Other than the proof being incomplete by not showing an Turing state machine, I cannot think of any flaws in the proof. I would appreciate any help with this problem as I have spent hours on it and don't seem to be making any progress.
Many thanks in advance!