I'm reading this book about the biography of Zero, and for all the math-geeks out there its actually pretty interesting. It talks about the evolution of math theory, and some of the politics along the way between science and religion (the "universal war" I suppose).
One of the main issues with Zero's adoption was the duality of nothing and infinity. While we understand the concepts now, back in the day people couldn't grasp it - or wouldn't. The book carries many stories about how math'ies started to develop ways to convince people to embrace zero/infinity. Lo and behold, one of the stories involves what is known as The Harmonic Series:
1/1 + 1/2 + 1/3 + .... + 1/n
this is the mathematical expression that is graphically shown in the picture at the top. The question of the day was, what is the answer to this sum? This was questioned by some guy Zeno who postulated that if Achilles ran twice as fast as a rabbit, who had a 1m head start, he'd never catch up because he's always 'just behind'. Google it for details, but the short of it is that now we take limits and that clears up everything. Errthing.
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