Is an infinite sequence only defined on the positive integers or can it be defined on the negitive integers? My book gives the definition, "Any function u defiined for all positive integers from 1 to N is said to define a sequence of N terms, and u(n) is said to be the nth term of the sequence u." The book does not say anything about negitive integers, can you let me know if it is.
January 21st 2007, 01:03 PM
Are you making too much for this? By that I mean that the set of positive integers is used for convenience. It is a way of labeling a countable set. Negative integers are sometimes used particularly for sequences associated infinite series. But remember, any subset of integers can be mapped injectively to the positive integers.