Is there a word that relates to infinitesimal in the way that zero

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The discussion centers on the relationship between infinitesimal numbers and infinity, particularly in the context of the hyperreal number system. Participants clarify that in this system, infinitesimals and infinite numbers are reciprocals of each other, while zero remains undefined. The ordinary Real number system does not accommodate these concepts, leading to the reliance on limits in Calculus and Analysis. Understanding hyperreal numbers requires advanced theoretical knowledge.

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Is there a word that relates to infinitesimal in the way that zero relates to infinity?
 
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Pjpic said:
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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