0 vs. nothing is one of those abstract distinctions that’s almost impossible to talk about directly; you more have to do it with examples. Imagine there’s a certain math class, and in this class there’s a fiendishly difficult 100-point midterm, and imagine that neither you nor I get even one point out of 100 on this exam. Except there’s a difference: you are not in the class and didn’t even take the exam, where as I am, and did. The fact that you received 0 points on the exam is thus irrelevant — your 0 means N/A, nothing — where are my 0 is an actual zero. Or if you don’t like that one, imagine that you and I are respectively female and male, both healthy and 20—40 years of age, and we’re both at the doctor’s, and neither of us has had a menstrual period in the past ten weeks, in which case my total number of periods is nothing, whereas yours here is 0 — and significant.
From Everything and More: A Compact History of Infinity (Great Discoveries)