Thomas-Finney defines a bounded sequence as follows: - A sequence an is said to be bounded if there exists a real number M such that |an| ≤ M for all n belonging to natural numbers. This is equivalent to saying -M ≤ an ≤ M So, if all terms of a sequence lies between, say -1 and 1, i.e. in the interval (-1,1), then its bounded. But what if all values of an lies between, say -3 and 1, i.e in the interval (-3,1)? Is it still bounded? By the above definition it isn't. Essentially what I'm asking is whether the definition can be N ≤ an ≤ M , for some N belonging to real numbers? Thanks.