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Full Idea
It is possible, without the notion of unity, to define what is meant by one-to-one.
Gist of Idea
We can define one-to-one without mentioning unity
Source
Bertrand Russell (The Principles of Mathematics [1903], §109)
Book Ref
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.113
A Reaction
This is the trick which enables the Greek account of numbers, based on units, to be abandoned. But when you have arranged the boys and the girls one-to-one, you have not yet got a concept of number.
| 15916 | Frege's one-to-one correspondence replaces well-ordering, because infinities can't be counted [Frege, by Lavine] |
| 17446 | Counting rests on one-one correspondence, of numerals to objects [Frege] |
| 9582 | Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege] |
| 17444 | Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck] |
| 14118 | We can define one-to-one without mentioning unity [Russell] |
| 9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
| 17450 | Understanding 'just as many' needn't involve grasping one-one correspondence [Heck] |
| 17451 | We can know 'just as many' without the concepts of equinumerosity or numbers [Heck] |