Ideas from 'works' by Karl Weierstrass [1855], by Theme Structure

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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals

18086

Weierstrass eliminated talk of infinitesimals

			Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors.
			From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits

18092

Weierstrass made limits central, but the existence of limits still needed to be proved

			Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits.
			From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4
			A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts.