std::is_sorted and strictly less comparison?

Question

I do not understand well the std::is_sorted algorithm and its default behaviour. If we look to cppreference, it says that by default std::is_sorted uses the < operator. Instead of that, I find that using <= would be natural. But my problem is that for the following list of numbers :

1 2 3 3 4 5

it will return true, even if 3 < 3 should be false. How is that possible ?

EDIT: its seems to be worse than what I thought, because passing std::less_equal<int> will return false in that case... What is the condition applied when I pass a comparator function?

Answer 1

Per 25.4/5:

A sequence is sorted with respect to a comparator comp if for any iterator i pointing to the sequence and any non-negative integer n such that i + n is a valid iterator pointing to an element of the sequence, comp(*(i + n), *i) == false.

So, for

1 2 3 3 4 5

std::less<int>()(*(i + n), *i) will return false for all n, while std::less_equal will return true for case 3 3.