more from Stewart Shapiro

Single Idea 8763

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number]

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.