Full Idea
Zero is the extension of 'is equinumerous with the concept "is not self-identical"' (which holds of no objects); ..one is defined as the extension of 'is equinumerous with the concept "is identical to zero"'.
Clarification
The 'extension' is the members of that set
Gist of Idea
Zero is defined using 'is not self-identical', and one by using the concept of zero
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Joan Weiner - Frege Ch.4
Book Reference
Weiner,Joan: 'Frege' [OUP 1999], p.66
A Reaction
It sounds like some sort of cheating to define zero in terms of objects, but one in terms of concepts.