If a sequence has a definite number of terms, it is said to be finite, a word meaning limited. But a sequence may have an unending number of terms. For example, the integers of the number system go on forever: if you counted to one billion you could just as well count to one billion and one. You can easily imagine 1021 It is just as possible to imagine the number 1021 1. Such a sequence is said to be infinite: it is unlimited.