Full Idea
It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures.
Clarification
See under 'Types of Number' for explanations of these terms
Gist of Idea
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex
Source
Stewart Shapiro (Thinking About Mathematics [2000], 10.2)
Book Reference
Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.267
A Reaction
The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed.