Do not try too hard to compare with maths here. A programming language is different in many things from how maths is usually formalized. In C++20 there is no "s

Do not try too hard to compare with maths here. A programming language is different in many things from how maths is usually formalized. In C++20 there is no "strong total ordering", "weak total ordering" nor their partial counterparts. There are just "strong ordering", "weak ordering" and "partial ordering". In a strong ordering, two objects can only by one smaller, equal or larger than the other. If they are equal, it means that they are substitutable. In a weak ordering, two objects can only be one smaller, equivalent or larger than the other. No substitutability is implied. In a partial ordering, two objects can be one smaller, equivalent or larger than the other, or just not comparable. Again, no substitutability is implied. There is no point in distinguishing strict vs non-strict: depending on whether you call < or <= you will get the string or not string variant, and the same for > and >=.