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Ideas of Augustin-Louis Cauchy, by Text

[French, 1789 - 1857, Professor at École Polytechnique.]

1821	Cours d'Analyse

p.19	p.247	18085	Values that approach zero, becoming less than any quantity, are '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.
			From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4
			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.

p.19	p.247	18084	When successive variable values approach a fixed value, that is its 'limit'
			Full Idea: When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others.
			From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4
			A reaction: This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction?