 Kilvington’s concept of infinity is one of his greatest achievements. He takes for granted Ockham’s definition of a continuum, according to which each continuum is a being that contains an actually infinite number of smaller and smaller proportional parts. When we are given any continuum, we are also given its halves, the halves of these halves and, consequently, Ockham claims, an infinite number of its parts. The actual infinity is not understood here as an actually infinite continuum “that is so great that there cannot be any greater one”. Thus, it is impossible for a process of infinite division to be accomplished, for if it were accomplished, it would no longer be infinite, but finite. For Ockham, an actually infinite continuum is a set of actually existing parts which could be enumerated without end. Kilvington supports Ockham’s view in all his works, starting from Sophismata up to the commentary on the Sentences. Ockham, however, never gives any mathematical proof for this statement and limits himself to exploring Duns Scotus’s geometrical arguments against indivisibility. Kilvington puts more effort into demonstrating that infinite proportional parts actually exist in a continuum (S 42[43]: 112–15; Kretzmann 1990b: 307; see also Jung &amp; Podkoński 2009a; Podkoński 2016). In his philosophical and theological works, Kilvington provides many examples proving that infinite sets are not equal, that is, that they are not of the same density. He also explains how to establish a one-to-one correspondence of the elements of such infinite sets. Kilvington affirms that all created infinities, being infinite, are equal ‘in multitude.’ This, however, does not imply that infinities are necessarily equal ‘in magnitude’, since two created infinities can be at once equal and unequal with respect to multitude of their parts or their dimensions. Infinities can also be ‘qualitatively’ unequal because there is a qualitative difference between God’s infinity and every created being’s infinity. God as the most perfect is the only being absolutely infinite, whereas creatures as contingent beings can only be relatively infinite. As Podkoński affirms “Kilvington must have been convinced that an infinite set can be put in one-to-one correspondence with infinite subsets. And it is worth noting that this paradoxical feature of infinite sets nowadays serves as a criterion of determining them” (see Podkoński 2009: 142).