more from this thinker | more from this text
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
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] |