[shadowlight]

>Nope, you don't need the axiom of choice to define the sequence of all algorithms.

No. I'm saying selecting an algorithm out of the set of all algorithms.

I'm not saying defining the set of all algorithms.

[rocqua]

Putting the set of all algorithms in an order is quite easy. Like the comment above suggests. Just put them in alphabetical / lexicographical order.

Then you don't need to "randomly pick" an algorithm. You just start with the first algorithm in the sequence, and keep going.

[shadowlight]

As my retort to that common mentioned, he is wrong.

That is still random. You are arbitrarily picking an encoding, (English) in this case. Why not a Russian programming language or Chinese? How did you *select* your encoding out of the set of all encodings?

The act of assigning order to an unordered set is arbitrary. ABC order is a made up concept. It's not numerical, it's an arbitrary language and an arbitrary order that's a by product of human culture. Thus invoking this is at it's essence invoking the axiom of choice. You are arbitrarily selecting an algorithm.