Full Idea
Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3.
Clarification
'Null' is the empty set, usually represented by Greek phi
Gist of Idea
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3
Source
Stewart Shapiro (Thinking About Mathematics [2000], 10.2)
Book Reference
Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.265
A Reaction
See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them.
Related Idea
Idea 645 If two is part of three then numbers aren't Forms, because they would all be intermingled [Aristotle]