In mathematics, infinitesimals or infinitesimal numbers are quantities are closer to zero than any standard real number, are not zero.
Infinitesimals are a basic ingredient in the procedures of infinitesimal calculus as developed by Leibniz, including the law of continuity and the transcendental law of homogeneity.
The insight with exploiting infinitesimals was entities could still retain certain specific properties, such as angle or slope, even though these entities were infinitely small.
The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the “infinity-th” item in a sequence.
The idea of infinitesimals was originally introduced around 1670 by either Nicolaus Mercator or Gottfried Wilhelm Leibniz.
As Cantor and Dedekind were developing additional abstract versions of Stevin’s continuum, Paul du Bois-Reymond wrote a series of papers on infinitesimal-enriched continua established on growth rates of functions.
Some Points about Infinitesimals:
The idea suggests a thought experiment of adding an infinite number of parallelograms of infinitesimal width to form a finite area.
😊In the 20th century, it was found infinitesimals could serve as a basis in support of calculus and analysis.
😊The English mathematician John Wallis introduced the expression 1/∞ in his 1655 book Treatise on the Conic Sections.
😊The symbol, which denotes the reciprocal, or inverse, of ∞, is the symbolic representation of the mathematical idea of an infinitesimal.
😊The Greek mathematician Archimedes , in The Method of Mechanical Theorems, was the first to propose a logically rigorous definition of infinitesimals.
😊When Newton and Leibniz invented the calculus, they made use of infinitesimals, Newton’s fluxions and Leibniz’ differential.
😊This idea was the predecessor to the modern method of integration usual in integral calculus.
😊Mathematicians, scientists, and engineers continued to use infinitesimals to produce correct results.
😊A number system is said to be Archimedean if it contains no infinite or infinitesimal members.
Source:
[1] Wikipedia Contributors. “Infinitesimal.” Wikipedia, Wikimedia Foundation, 29 Sept. 2020, en.wikipedia.org/wiki/Infinitesimal. Accessed 5 Nov. 2020.
[2] TheDigitalArtist. “Geometry Math Shape – Free Photo on Pixabay.” Pixabay.Com, 19 July 2017, pixabay.com/photos/geometry-math-shape-geometric-2520247/. Accessed 5 Nov. 2020.