[1] Note that two elements may be equivalent without being equal. One standard example is sorting a sequence of names by last name: if two people have the same last name but different first names, then they are equivalent but not equal. This is why stable_sort is sometimes useful: if you are sorting a sequence of records that have several different fields, then you may want to sort it by one field without completely destroying the ordering that you previously obtained from sorting it by a different field. You might, for example, sort by first name and then do a stable sort by last name.

[2] Stable_sort uses the merge sort algorithm; see section 5.2.4 of Knuth. (D. E. Knuth, The Art of Computer Programming. Volume 3: Sorting and Searching. Addison-Wesley, 1975.)