more from Augustin-Louis Cauchy

Single Idea 18085

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals]

Full Idea

When the successive absolute values of a variable decrease indefinitely in such a way as to become less than any given quantity, that variable becomes what is called an 'infinitesimal'. Such a variable has zero as its limit.

Gist of Idea

Values that approach zero, becoming less than any quantity, are 'infinitesimals'


Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4

Book Reference

Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.247

A Reaction

The creator of the important idea of the limit still talked in terms of infinitesimals. In the next generation the limit took over completely.