[shadowlight]

This is the weird fuzzy part with math.

I can say arbitrary stuff like the set of all sets with positive numbers but when I say the set of all algorithms written in English and C++ suddenly I'm getting too specific. Where is the line drawn?

[tshaddox]

I’m not sure what you mean. There’s nothing too specific about that.

[shadowlight]

Your assuming all algorithms are defined in terms of English that's how you can order them alphabetically. English is an arbitrary language that comes from human culture. Same with a programming language. You are defining a set in terms of concepts that are cultural.

Algorithms themselves have no specific order. In order to define enumeration you must first start off by *selecting* which algorithm gets the first enumeration. This is a completely arbitrary choice.