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

[the conclusion of a converging series]

5 ideas
Quantities and ratios which continually converge will eventually become equal [Newton]
When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock]
If x changes by less and less, it must approach a limit [Dedekind]
Theorems about limits could only be proved once the real numbers were understood [Maddy]