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Single Idea 18171

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite]

Full Idea

Both Cantor's real number (Cauchy sequences of rationals) and Dedekind's cuts involved regarding infinite items (sequences or sets) as completed and subject to further manipulation, bringing the completed infinite into mathematics unambiguously.

Gist of Idea

Cantor and Dedekind brought completed infinities into mathematics


Penelope Maddy (Naturalism in Mathematics [1997], I.1 n39)

Book Reference

Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.15

A Reaction

So it is the arrival of the real numbers which is the culprit for lumbering us with weird completed infinites, which can then be the subject of addition, multiplication and exponentiation. Maybe this was a silly mistake?

Related Idea

Idea 18150 Actual measurement could never require the precision of the real numbers [Bostock]