In Cauchy's 1821 terminology, an infinitesimal is a variable quantity tending to zero. Other mathematical frameworks give different precise meanings to the word; the intended framework must be specified.[ref]
Cours d'analyse by Augustin-Louis Cauchy. Chapter II
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Infinitesimal refers to a quantity that is extremely small, approaching zero but never actually reaching it. In mathematics, infinitesimals are used in calculus, particularly in the formulation of derivatives and integrals. In the context of non-standard analysis, developed by mathematician Abraham Robinson in the 1960s, infinitesimals can be rigorously defined and treated like real numbers, allowing for a formal approach to concepts that describe quantities that are smaller than any positive real number.
