What is singular and non-singular values in the context of STL iterators?

Question

The section §24.1/5 from the C++ Standard (2003) reads,

Just as a regular pointer to an array guarantees that there is a pointer value pointing pa

Answer 1

If I understand this correctly, a singular value for an iterator is essentially the equivalent of an unassigned pointer. It's an iterator that hasn't been initialized to point anywhere and thus has no well-defined element it's iterating over. Declaring a new iterator that isn't set up to point to an element of a range, for example, creates that iterator as a singular iterator.

As the portion of the spec alludes to, singular iterators are unsafe and none of the standard iterator operations, such as increment, assignment, etc. can be used on them. All you can do is assign them a new value, hopefully pointing them at valid data.

I think the reason for having this definition is so that statements like

set::iterator itr;

Can be permitted by the spec while having standardized meaning. The term "singular" here probably refers to the mathematical definition of a singularity, which is also called a "discontinuity" in less formal settings.