Explore: Infinitely Small

when used as an adjective in mathematics, infinitesimal means infinitely small, smaller than any standard real number. Infinitesimals are often compared

began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity

differential dy as an infinitely small (or infinitesimal) change in the value y of the function, corresponding to an infinitely small change dx in the function's

differential dx represents an infinitely small change in the variable x. The idea of an infinitely small or infinitely slow change is, intuitively, extremely

follows: ...the supposition that bodies can be imagined which, for infinitely small thicknesses, completely absorb all incident rays, and neither reflect

limits. Infinitesimals get replaced by sequences of smaller and smaller numbers, and the infinitely small behavior of a function is found by taking the limiting

infinitesimals implies the introduction of ideal numbers which might be infinitely small or infinitely large compared with the real numbers but which were to possess

{\displaystyle o} ⁠ is an infinitely small amount of time. So, the term ⁠ o 2 {\displaystyle o^{2}} ⁠ is second order infinite small term and according to

limits if, between these limits, an infinitely small increment in the variable always produces an infinitely small increment in the function itself. M

could not dispense with a treatment of the principal properties of infinitely small quantities, properties which serve as the foundation of the infinitesimal