more from this thinker | more from this text
Full Idea
A system S is said to be infinite when it is similar to a proper part of itself.
Clarification
We would now call a 'system' a 'set'
Gist of Idea
A system S is said to be infinite when it is similar to a proper part of itself
Source
Richard Dedekind (Nature and Meaning of Numbers [1888], V.64)
Book Ref
Dedekind,Richard: 'Essays on the Theory of Numbers' [Dover 1963], p.63
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] |