The mathematical meaning of the word "infinity " is so well know that there is a tendency to overlook or neglect its metaphysical meaning, but it is the latter that is of prime importance in philosophical theology. Among the negative attributes of the supreme being is God's infinity. The supreme being is not only eternal (nontemporal) and immaterial, but also infinite.
In mathematics, we deal with potential infinities. For example, the series of whose numbers is endless. To any integer, no matter how large, another integer can be added. Between any two whole numbers is an infinite series of fractions. There is no pair of fractions, so small that smaller fractions cannot be found. This potential infinite is the infinitesimal. To call these two infinities potential is to say that addition or division can go on endlessly. There is no actually infinite number.
When we say of the supreme being that God is actually infinite, as no physical thing is, not even the whole physical cosmos, we have a quite different meaning of the word "infinite" in mind. A thing differs in kind from things of another kind. Each belongs to a class that exclude other classes. Each lacks the traits that differentiate it from other individuals within the class of which both are members.
The finiteness of all the things of the physical cosmos is revealed by the traits or properties that it lacks. But the supreme being is unique. There is only one supreme being. God is not the member of any class that excludes other classes; and God is not an individual differing from other individuals, all of which are members of a given class. That is what we mean when we say God is not finite His existence is unlimited.