Zeno's paradoxes
As one begins adding the terms in the series , one may notice that the sum gets closer and closer to 1, and will never exceed 1. Aristotle (who is the source for much of what we know about Zeno) noted that as the distance (in the dichotomy paradox) decreases, the time to travel each distance gets exceedingly smaller and smaller. Before 212 BCE, Archimedes had developed a method to get a finite answer for the sum of infinitely many terms which get progressively smaller (such as ).