User blog comment:Wythagoras/All my stuff/@comment-10429372-20130718073726/@comment-5529393-20130719041605

Yes, it seems like Dr. Ceasium is making "possible output" more general than what we are talking about.

Say we specify that the definition is written in a LaTeX file using ASCII characters - then for ¥(1000) we need to check the 128^1000 possible 1000 character files, discard the ones that don't define a single specific number, and from the rest choose the one the defines the maximum. There's no "larger possible output" outside of these 128^1000 possibilities.