An infinitesimal is a nonzero quantity whose absolute value is smaller than every positive real number. In nonstandard analysis, the convention usually includes 0 as an infinitesimal (Keisler 2007, p. 2). The infinitesimal monad of 0 uses this convention. The understanding of infinitesimals was a major roadblock to the acceptance of calculus and its placement on a firm mathematical foundation.
Infinitesimal
See also
Infinite, Infinitesimal Monad, Infinity, Nonstandard AnalysisExplore with Wolfram|Alpha
References
Bell, J. L. A Primer of Infinitesimal Analysis. Cambridge, England: Cambridge University Press, 1998.Keisler, H. J. Foundations of Infinitesimal Calculus. Online ed., 2007. Revised Jun. 19, 2022. https://people.math.wisc.edu/~hkeisler/foundations.pdf.Numberphile. "The Opposite of Infinity." Sep. 8, 2015. https://www.youtube.com/watch?v=WYijIV5JrKg.Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 1168, 2002.Referenced on Wolfram|Alpha
InfinitesimalCite this as:
Weisstein, Eric W. "Infinitesimal." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Infinitesimal.html