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

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9 ideas
Things get smaller without end [Anaxagoras]
A tangent is a line connecting two points on a curve that are infinitely close together [Leibniz]
Nature uses the infinite everywhere [Leibniz]
Infinitesimals are ghosts of departed quantities [Berkeley]
Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy]
Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher]
Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock]
With infinitesimals, you divide by the time, then set the time to zero [Kitcher]
Infinitesimals do not stand in a determinate order relation to zero [Rumfitt]