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Single Idea 14134

[filed under theme 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 Ref

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

The 3 ideas with the same theme [what is distinctive about infinite numbers?]:

9826 A system S is said to be infinite when it is similar to a proper part of itself [Dedekind]
7556 A collection is infinite if you can remove some terms without diminishing its number [Russell]
14134 Infinite numbers are distinguished by disobeying induction, and the part equalling the whole [Russell]