Epsilontic – Limits and Continuity
I remember that I had some difficulties moving from school mathematics to university mathematics. From what I read on PF through the years, I think I’m not the only one who struggled at that point. We mainly learned algorithms at school, i.e. how things are calculated. At university, I soon met a quantity called epsilon. Algorithms became almost obsolete. They used ##\varepsilon ## constantly but all we got to know was that it is a positive real number. Some said it was small but nobody said how small or small compared to what. This article is meant to introduce the reader to a world named epsilontic. There is quite a bit to say and I don’t want to bore readers with theoretical explanations. I will therefore try to explain the two basic subjects, continuity and limits, in the first two sections in terms a high school student can understand, and continue with the theoretical considerations afterward.