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
Source
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]