I'm not really sure if this would go in homework or the calculus and analysis forums, so if I picked the wrong one please correct me. My calculus book has an example worked out that confused me, but you have to use the example to do the problems, which is why I put it here. (Note: Since I don't know how to use LaTeX, I will just use the notation abs(x) for the absolute value of x, and e and o for epsilon and delta respectivly.) 1. The problem statement, all variables and given/known data It is proving that the function f(x)=x2 approaches 9 near 3. I'm going to start writing what the book says now. We must ensure that abs(x2-9)<e for any given positive e. The obvious first step is to write: abs(x2-9)=abs(x-3)*abs(x+3). We require that abs(x-3)<1, which gives us abs(x+3)<7, which gives us: abs(x-3)*abs(x+3)<7abs(x-3) [I verified that this inequality is true, everything up to this point makes perfect sense to me, we're just choosing our specific deltas.] This shows us we have abs(x2-9)<e for abs(x-3)<1, [Yes it does] and abs(x-3)<e/7; or officially, we require abs(x-3)<min(e/7,1). Wait just a second. 2. Relevant equations Since this is a proof, there really aren't any. 3. The attempt at a solution I understand everything before my comment, "yes it does." However, if e=7abs(x-3), then e/7 would be abs(x-3), which is saying abs(x-3)<abs(x-3), which is ridiculous! Is this a typo, or did I truly miss something? Thank you for your help.