Why is the default set implementation ordered in the first place? The formal data structure is unordered, which probably informs people's assumptions about its performance characteristics. Should it not be "set" and "ordered_set"?
"Sorted" rather than ordered (an order can be arbitrary and I'd personally associate the word with insertion order).
> The formal data structure is unordered
The formal data structure doesn't have complexity bounds, the STL does.
If/when `std2::` happens, this is one of the things I assume would change.