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Single Idea 18180

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers ]

Full Idea

Von Neumann's version of the natural numbers is in fact preferred because it carries over directly to the transfinite ordinals.

Gist of Idea

Von Neumann numbers are preferred, because they continue into the transfinite

Source

comment on John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n9

Book Ref

Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.24

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The 4 ideas with the same theme [Von Neumann's view of numbers as expanding sets]:

18179

For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]

18180

Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]

15925

Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]

10997

Von Neumann numbers are helpful, but don't correctly describe numbers [Read]