1. The problem statement, all variables and given/known data The problem and its solution is attached. 2. Relevant equations Big-O notation. 3. The attempt at a solution I get how to do this problem. The reason I'm making this post is for little details about the constants c and n_0. To my knowledge both c and n_0 have to be greater than 0. For n_0, if you use the definition of natural numbers which excludes 0 then I have no problem. On the other hand, the constant c being any real implies that it can be 0 or a negative number as well which doesn't fit in well with what I have learned. Am I wrong or is the solution wrong? What are the subtleties here?