Passage: To be assigned an Erdős number, someone must be a coauthor of a research paper with another person who has a finite Erdős number.  Paul Erdős has an Erdős number of zero. Anybody else's Erdős number is k + 1 where k is the lowest Erdős number of any coauthor.  The American Mathematical Society provides a free online tool to determine the Erdős number of every mathematical author listed in the Mathematical Reviews catalogue.Erdős wrote around 1,500 mathematical articles in his lifetime, mostly co-written. He had 511 direct collaborators; these are the people with Erdős number 1.  The people who have collaborated with them (but not with Erdős himself) have an Erdős number of 2 (11,009 people as of 2015), those who have collaborated with people who have an Erdős number of 2 (but not with Erdős or anyone with an Erdős number of 1) have an Erdős number of 3, and so forth. A person with no such coauthorship chain connecting to Erdős has an Erdős number of infinity (or an undefined one). Since the death of Paul Erdős, the lowest Erdős number that a new researcher can obtain is 2.

Question: What is not being defined?
Erdős number of infinity