Recently, the make-up exam was promoted to advanced mathematics (1), and the proportion of calculus with one variable function in the test questions is very large. In 2007 and 2006, the test scores were about 1 10.
The positive number ε is used to describe the distance between the term xn of the sequence and the constant a. If xn takes a as the limit, this distance can be arbitrarily small in the process of n→∞. ε has nothing to do with the sequence xn and is not fixed, so it can be understood as a variable.
The positive integer n is determined by and depends on ε, indicating the subscript of an item in the sequence, indicating that all items in the sequence satisfy | xn-a | < ε from a certain item, that is, only finite items do not satisfy | xn-a | < ε.