Well, you do not seem to know all of the meanings of the word 'partial functions'. If one types in 'partial function' in google one can see both the meaning 'partial function' that you have in mind and the meaning of 'partial function' that the article talks about on the first result page. In fact, the 'partial function' of the article appears as the first result. 'CONFUSING' says more about you than about the article.