The following image is from Page 346 of chapter 12 of Tom M Apostol Mathematical Analysis. I have a question in the underlined part.
Question is -> What does author means by statement that error term is of smaller order than h? What is use/ meaning of the word " order " here?
That an error term $\phi(h)$ is of smaller order than $h$ means that the relative error $\dfrac{\phi(h)}{h} \to 0$ as $h \to 0$. In other words, the error term goes much faster to $0$ as $h$.