Please explain what an infinitesimal is, without using circular logic, and so that things such as a sum of a series will make sense given the definition.
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Anonymous2010-01-03 0:52
>Please explain what an infinitesimal is
There was never a water-tight mathematical definition of an infinitesimal (as used by Newton, etc); the notion made sense to mathematicians only on an intuitive level. In the 19th century the epsilon-delta definition of a limit was invented, which made sense mathematically, and could be used in calculus instead of infinitesimals.