Background: mechanical engineer with a flawed math education (and trying to make up for it). I have recently read this statement (and others like it): "We shall also informally use terminology such as "infinitesimal" in order to avoid having to discuss the (routine) "epsilon-delta" analytical issues that one must resolve in order to make these integration concepts fully rigorous." Could someone elaborate on what this means? I the cloud of my memory, I see all these words as ONE CONCEPT on a path toward learning integration. Were there actually TWO ways I was taught, which, over the years, I got all jumbled up in my head? Is one more rigorous that the other? What does the author mean when he puts the word "routine" in parentheses (they are his, not mine).