more from this thinker | more from this text
Full Idea
The cardinal number of M is the general idea which, by means of our active faculty of thought, is deduced from the collection M, by abstracting from the nature of its diverse elements and from the order in which they are given.
Gist of Idea
A cardinal is an abstraction, from the nature of a set's elements, and from their order
Source
George Cantor (works [1880]), quoted by Bertrand Russell - The Principles of Mathematics §284
Book Ref
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.304
A Reaction
[Russell cites 'Math. Annalen, XLVI, §1'] See Fine 1998 on this.
Related Idea
Idea 9145 We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor]
| 14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
| 14146 | We aren't sure if one cardinal number is always bigger than another [Russell] |
| 13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
| 17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
| 17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| 17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck] |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |