The concept of infinity is hard to grasp because it is an abstraction. There are no tangible objects in our lives that are truly infinite in number so we really have nothing to compare it to. The only way to get an infinite number of anything is by invoking infinity elsewhere, which doesn’t really clarify matters much.

For example, the number of elementary particles in our visible universe, although immensely large, is still a finite number. If we assume that the density of particles in the universe is roughly the same everywhere and *further postulate that the universe is of infinite size*, then we can arrive at an infinite number of particles. But now we have the problem of understanding what a universe of infinite size is like.

If the concept of infinity is not hard enough, it turns out that there is not just one infinity but an infinite number of infinities of different sizes, so to speak.

I thought this video does an excellent job of trying to explain these difficult abstractions.