Full Idea
Frege defines numbers in terms of 'equinumerosity', which says two concepts are equinumerous if the items falling under one of them can be placed in one-to-one correspondence with the items falling under the other.
Gist of Idea
Numbers are definable in terms of mapping items which fall under concepts
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Roger Scruton - Short History of Modern Philosophy Ch.17
Book Reference
Scruton,Roger: 'A Short History of Modern Philosophy' [ARK 1985], p.246
A Reaction
This doesn't sound quite enough. What is the difference between three and four? The extensions of items generate separate sets, but why does one follow the other, and how do you count the items to get the one-to-one correspondence?