Empirical collections to which we attach a number, such as the plates on a person's table at dinner time, are, for Frege, concealed concepts, given by description. An example would be the concept17: "plate on my table at dinner time".
Motivation for Frege's precise definition of number is given, in a very simple way, from the content neutrality of number. For the number 5, say, is not attached to any particular concept F under which 5 things fall, for that would make 5 depend on the qualitative content of F. Instead, 5 has to apply to all such concepts, with no favoritism18, and this leads to Frege's famous definition of number which runs as follows: the number which belongs to the concept F is the extension of the concept "equinumerous to the concept F".
The Hegelian concept is at a much more general level than the Fregean. For Hegel, "the collection of knives on the table at dinner time" would not, I think, even have counted as a concept, as it did for Frege. Indeed, we would naturally think of pointing out the collection of knives rather than contemplating it. However, there is no doubt that there is conceptual content in the description of this collection (e.g. the concept of knife) and so for the rest of the paper, we will ignore this difererence between the Hegelian and Fregean concept.