 Oresme was not the first to use the principle of one-to-one correspondence in discussing the properties of actual infinites. Bradwardine, whose main aim was to refute Aristotle’s opinion that the world is eternal, applied the principle of one-to-one correspondence to show that two infinites would be equal or – in modern terms – that an infinite subset is equal to the set of which it is a part (Bradwardine 1618, 121C–124C). On the other hand Bradwardine takes it for granted that an infinite subset is smaller than the set of which it is a part. Thus he is of the opinion that under the assumption of an eternal world that has no beginning the multitude of all human souls, which until now have been created, must be greater than the multitude of the male or the female souls alone (Bradwardine 1618, 132E–133A). From this contradiction – an infinite subset cannot be both smaller than and equal to the set of which it is a part – Bradwardine draws the inference that the eternity of the world is impossible (Thakkar 2009, 626–629).