Zeno of EleaZeno of Elea was born in Elea, Italy, in 490 BC. He died there in 430 BC, in an attempt to oust the city's tyrant. He was a renowned student of Parmenides, from whom he learned most of his doctrines and political ideas. He believed that what exists is one, permanent and unchanging. Zeno opposed multiplicity and movement. He did this by showing the contradictions that result from assuming they were real. His argument against multiplicity stated that if the multiple exists, it must be both infinitely large and infinitely small, and it must be both limited and unlimited in number. His argument against movement is characterized by two famous illustrations: the flying arrow and the runner in the race. It is the illustration with the runner which is associated with the first part of the assignment. In this illustration, Zeno argued that a runner can never reach the end of a running course. It specifies that the runner first completes half the course, then half the remaining distance, and will continue to do so ad infinitum. In this way, the runner will never be able to reach the end of the course, because it would be infinitely long, just as the semester would be infinitely long if we did half of it, then half of the rest, ad infinitum. This interval will diminish infinitely, but will never completely disappear. This type of argument can be called the antinomy of infinite divisibility and was part of the dialectic invented by Zeno. These are, however, only a small part of Zeno's arguments. He is believed to have devised at least forty arguments, eight of which have survived to the present day. Although these arguments seem simple, they have managed to raise a number of deep philosophical and scientific questions about space, time and infinity, throughout history. These questions still interest philosophers and scientists today. The problem with Zeno's argument and yours is that neither of you are interested in adding infinity. Your argument suggests that if we add infinity, the sum will be infinity, which is not the case.