Is there a word that relates to infinitesimal in the way that zero relates to infinity?
I don't think that zero does relate to infinity.
In the hyperreal number system, there are two kinds of non-real numbers: infinitesimal and infinite. The reciprocal of any infinitesimal number is infinite. The reciprocal of any infinite number is infinitesimal. The inverse of zero is still undefined.
In the ordinary Real number system, there are neither infinite nor infinitesmal numbers. That's why most Calculus and Analysis deal with derivatives in terms of limits rather than infinitesmals. It takes some deep theory to be able to define the "hyperreals" that tac-tics refers to.
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