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Full Idea
Even the fundamental theorems about limits could not [at first] be proved because the reals themselves were not well understood.
Gist of Idea
Theorems about limits could only be proved once the real numbers were understood
Source
Penelope Maddy (Naturalism in Mathematics [1997], I.2)
Book Ref
Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.27
A Reaction
This refers to the period of about 1850 (Weierstrass) to 1880 (Dedekind and Cantor).
18082 | Quantities and ratios which continually converge will eventually become equal [Newton] |
18084 | When successive variable values approach a fixed value, that is its 'limit' [Cauchy] |
18092 | Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock] |
18087 | If x changes by less and less, it must approach a limit [Dedekind] |
18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
22886 | The modern idea of 'limit' allows infinite quantities to have a finite sum [Bardon] |