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 Reference
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.