Your own example used the word "alphabetical." So your example is false because it uses a "particular" encoding.
Try to select an algorithm out of the set of all algorithms without using an encoding. If you must use an encoding, please ensure that it's not a "particular" encoding.
You can't.
The point is all encodings in the known universe are "particular."
Additionally, to even use an encoding you have to *select* and encoding from the set of all encodings.
Yes, I chose one arbitrary method of enumeration. That’s not important to the point, which is that algorithms are enumerable and thus you don’t need the axiom of choice to select one out of the set of all algorithms.
Try to select an algorithm out of the set of all algorithms without using an encoding. If you must use an encoding, please ensure that it's not a "particular" encoding.
You can't.
The point is all encodings in the known universe are "particular."
Additionally, to even use an encoding you have to *select* and encoding from the set of all encodings.