The concept of infinity is an extremely useful mathematical tool, primarily used in physics (and in many other sciences where mathematical tools are employed). In reality, the idea of infinity is present even outside of mathematics, not merely as an abstract concept. For instance, one may wonder whether the universe is finite or infinite, but this question (at least for now) remains one to which we are unable to provide a certain answer.
Returning to infinity in mathematics, it is rigorously defined (as one would expect for any mathematical tool). Let’s consider a very simple example, the natural numbers: they are infinite in number. No matter what number I can think of, it is always possible to think of a larger number.
However, no matter how much larger a number I can think of, it will still be a “finite” number (albeit a very large one) simply because I can think of it (and express it). That is, infinity does not truly exist, except as an unreachable upper limit of a quantity we cannot reach. Because if we were to reach it, then it wouldn’t be infinite; it would become finite.
Should we, therefore, abolish the concept of infinity? Certainly not. But we cannot consider it as a genuinely existing entity, something that finds a correspondence in the physical world. Unless, of course, the universe is truly infinite…
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