Infinity as first known in mathematics is a property of finite quantities. Euclid, for example, proves prime numbers are infinite because, given any amount of them, another can be found. Obviously, no one can argue that finite quantities are infinite in the sense that a definite number of things is actually not a definite number; rather the sense is that a finite series is such that there is always another possible member.
But isn’t every species like that to its members? Perhaps, but among material things the limit to the number of members is the material they are made out of. There’s nothing about the definition of bread that fixes how many loaves there can be, but there is a hard limit set by how much dough one has. When we abstract from just this sort of material to make a mathematical thing, the resulting species is essentially infinite, which means that, for example, while there can be a real sense to Eighteenth Century French peasants running out of bread, there can be no sense to math running out of instances of the number three.
This is one approach to Aristotle’s insight that the infinite is essentially a part, i.e. it is a finite series whose last member is recognized as not essentially a last member. The fourth side of a square is the last side it can have, but the fourth extension of a straight line or the fourth prime number you find are not the last extension or prime. The infinite is the recognition of the absence of essential terminus, or a recognition of the contingency of a terminus.
The infinite is thus first of all a recognition of one more or the essential partiality of any series, while the universal is whole, even where it recognizes the possibility of the infinite. The universal is thus greater than the infinite precisely because of the common notion that the whole is greater than the part.