[BITList] Maths made more difficult - Infinity

[HUGH]

John,

The hard bit is establishing "a series of approximations that converge", ie, that the series does converge, otherwise it is useless. Bizzare results have come from apparently converging series that do not converge.  The Greeks' objections were less to do with infinity than with infinitesimals.  They bothered them, eg, how could a finite quantity suddenly become zero?  The method attributed to Archimedes was said by the man himself to belong to a predecessor, Eudoxus.  Simply put - if we have two numbers, neither of them zero, we can find a multiple of one that will exceed the other. That, believe it or not, is it.

Hugh.
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