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Single Idea 22716

[from 'works' by John von Neumann, in 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers ]

Full Idea

At age twenty, Von Neumann devised the formal definition of ordinal numbers that is used today: an ordinal number is the set of all smaller ordinal numbers.

Gist of Idea

Von Neumann defined ordinals as the set of all smaller ordinals

Source

report of John von Neumann (works [1935]) by William Poundstone - Prisoner's Dilemma 02 'Sturm'

Book Reference

Poundstone,William: 'Prisoner's Dilemma' [OUP 1992], p.29


A Reaction

I take this to be an example of an impredicative definition (not predicating something new), because it uses 'ordinal number' in the definition of ordinal number. I'm guessing the null set gets us started.