The Greeks couldn't do this neat little mathematical trick. They didn't have the concept of a limit because they didn't believe in zero. The terms in the infinite series didn't have a limit or a destination; they seemed to get smaller and smaller without any particular end in sight. As a result, the Greeks couldn't handle the infinite. They pondered the concept of the void but rejected zero as a number, and they toyed with the concept of the infinite but refused to allow infinity-numbers that are infinitely small and infinitely large-anywhere near the realm of numbers. This is the biggest failure in Greek mathematics, and it is the only thing that kept them from discovering calculus."
( Charles Seife )
[ Zero: The Biography of a ]
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