  Notice that if concepts \(P\)  and \(Q\) are both concepts which satisfy one of these conditions, then there is a one-to-one correspondence between the objects which fall under \(P\) and the objects which fall under \(Q\). That is, if any of the above conditions accurately describes both \(P\) and \(Q\), then every object falling under \(P\) can be paired with a unique and distinct object falling under \(Q\) and, under this pairing, every object falling under \(Q\) gets paired with some unique and distinct object falling under \(P\). (By the logician’s understanding of the phrase ‘every’, this last claim even applies to those concepts \(P\) and \(Q\) which satisfy Condition (0).) Frege would call such \(P\) and \(Q\) equinumerous concepts (1884, §72). Indeed, for each condition defined above, the concepts that satisfy the condition are all pairwise equinumerous to one another.