 Thus, the number 0 becomes defined as the extension of all the concepts equinumerous to the concept not being self-identical.  This extension contains all the concepts that satisfy Condition (0) above, and so the number of all such concepts is 0. For example, the number of the concept being a square circle is \(0\), since nothing falls under it. Similarly, one could define the number \(1\) as the extension consisting of all the concepts that satisfy Condition (1) above, and define the number \(2\) as the extension of all the concepts that satisfy Condition (2) above, and so on.  But though this would define a sequence of entities which are numbers, this procedure doesn’t actually define the concept natural number (finite number).  Frege, however, had a deep idea about how to do this.