[jlarocco]

> Can you state this in a mathematically precise notation?

Big-O isn't meant to be precise. The entire point is to roughly describe algorithm behavior.

> 'Implied +C' is pretty much nonsense.

Implied +C is built in to the definition of big-O notation. As n increases towards infinity the influence of C becomes negligible, so it's left off. Read the first chapter of any algorithms book.