1. The problem statement, all variables and given/known data I am wondering if the general approach to these proofs involving absolute values and inequalities is to do them case-wise? Is that the typical approach (unless pf course you see some 'trick')? For example, I have: Prove that if |x-xo| < ε/2 and Prove that if |y-yo| < ε/2, then |(x+y)-(xo+yo)| < ε |(x-y)-(xo-yo)| < ε. It seems like there are way too many cases, but maybe that's just the way it is. For cases, I see: x=0, y=0 0 ≤ x, y≤0 oh jeesh .... forget listing them. I am now seeing that there are cases when xo is greater than or less than x (though I have a feeling that xo is supposed to be smaller than x and a positive number, but he (Spivak) did not specify...nor did he specify that ε > 0 though I think that it should be. Seems like these are gearing up for ε-δ proofs. Anyone have any thoughts on any of these points? This is problem 1.20 from Spivak's Calculus.