1. The problem statement, all variables and given/known data I'm referring to the question and solution for part (b) in the attached TheProblemAndSolution.jpg file. 2. Relevant equations Definition of limit. 3. The attempt at a solution Should the equation with the two things in brackets have absolute value bars instead of brackets? Also, according to this Wikipedia link ( http://en.wikipedia.org/wiki/Limit_of_a_sequence#Formal_Definition ), N should be a natural number and ϵ should be a real number but the solution in my book gives N as a function of ϵ, which means that it could be the case that N is also real and non-natural (such as an irrational number for example). Is there a contradiction here, or is there something I'm missing? Any input would be GREATLY appreciated!