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Single Idea 18178

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers ]

Full Idea

For Zermelo the successor of n is {n} (rather than Von Neumann's successor, which is n U {n}).

Gist of Idea

For Zermelo the successor of n is {n} (rather than n U {n})

Source

report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Naturalism in Mathematics I.2 n8

Book Ref

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

A Reaction

I could ask some naive questions about the comparison of these two, but I am too shy about revealing my ignorance.

The 3 ideas with the same theme [Zermelo's view of numbers as nested sets]:

18178 For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
15524 Zermelo's model of arithmetic is distinctive because it rests on a primitive of set theory [Lewis]
8762 Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]