More importantly for this audience, the idea of limits lies at the heart of numerical analysis. Explicating the quantifiers of the definition of a limit is the first step in obtaining control over any estimator of your data. This, among other things, is why I am perpetually baffled at the people in this audience who say that limits is something "they will never need". Limits, their algebra (which subsumes all of high school algebra and inequalities) and their delicate analysis is what makes a ton of numerical algorithms work; Higham's classic has it all, and is perfectly clear about it all.