Mathematicians have long held that infinite integers do NOT exist, but here is a very simple argument that shows that they do exist. A list of positive integers Z+ can be formed in a base-1 numeral system as... 1 11 111 1111 . . . 1111111... Since the set of integers is infinite, the list will be of an infinite length. If the length of the list is infinite, the last term will also be infinite in length since it is the same length as the list is long. If the term is infinite in the base-1 numeral system, then it will be infinite in base 2 or 10. Therefore infinite integers do exist.