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Single Idea 10573

[from 'Replies on 'Limits of Abstraction'' by Kit Fine, in 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number ]

Full Idea

Because of Dedekind's definition of reals by cuts, there is a bizarre modern doctrine that there are many 1's - the natural number 1, the rational number 1, the real number 1, and even the complex number 1.

Gist of Idea

Dedekind cuts lead to the bizarre idea that there are many different number 1's

Source

Kit Fine (Replies on 'Limits of Abstraction' [2005], 2)

Book Reference

-: 'Philosophical Studies' [-], p.386


A Reaction

See Idea 10572.

Related Idea

Idea 10572 A cut between rational numbers creates and defines an irrational number [Dedekind]