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Single Idea 14134

[from 'The Principles of Mathematics' by Bertrand Russell, in 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite ]

Full Idea

There are two differences of infinite numbers from finite: that they do not obey mathematical induction (both cardinals and ordinals), and that the whole contains a part consisting of the same number of terms (applying only to ordinals).

Gist of Idea

Infinite numbers are distinguished by disobeying induction, and the part equalling the whole

Source

Bertrand Russell (The Principles of Mathematics [1903], §250)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.260