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In the nineteenth century the German mathematician Karl Weierstrass introduced the epsilon-delta process, which provided a rigorous basis for Calculus and discouraged students from using the infinitesimal concept.
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The concept of infinitesimal had arisen with problems of a geometric character and infinitesimals were originally conceived as belonging solely to the realm of continuous magnitude as opposed to that of discrete number.
Thus, he provided preliminary concept of infinitesimal calculus.
The concept of infinitesimal was beset by controversy from its beginnings.
In recent years, however, the concept of infinitesimal has been refounded on a rigorous basis.
At first Berkeley poured scorn on those who adhere to the concept of infinitesimal.
The concept of infinitesimal parallel vector displacement is essential for doing calculus on manifolds.
Smooth infinitesimal analysis embodies a concept of intensive magnitude in the form of infinitesimal tangent vectors to curves.
By the beginning of the 20th century, the concept of infinitesimal had become, in analysis at least, a virtual "unconcept".
However useful it may have been in practice, the concept of infinitesimal could scarcely withstand logical scrutiny.
But from the algebra and analytic geometry of the 16th and 17th centuries there issued the concept of infinitesimal number.
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