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→What is an "Infinitesimal"?
''An infinitesimal is a framework for doing differential calculus'', nothing more. It involves two very small quantities having a functional relationship to each other, such that they both decrease toward zero simultaneously. Their ratio is the derivative.
''An infinitesimal is a framework for doing differential calculus'', nothing more. It involves two very small quantities having a functional relationship to each other, such that they both decrease toward zero simultaneously. Their ratio is the derivative.
If one really wants to point one's finger at a specific thing and call it an infinitesimal, in the "epsilon/delta" formulation of [[Limit_(mathematics)|limits]] the quantities <math>|f(x) - Y|</math> and <math>|x - X|</math> are the infinitesimals. These are, of course, not actual numbers, but expressions of dependency on <math>x</math> in the context of the derivative.
This concept was invented by Gottfried Leibniz with his "dx/dy" notation, and has been used ever since. Dx and dy are the infinitesimals. Isaac Newton's "fluxion" method of calculus did not involve this concept.
This concept was invented by Gottfried Leibniz with his "dx/dy" notation, and has been used ever since. Dx and dy are the infinitesimals. Isaac Newton's "fluxion" method of calculus did not involve this concept.