On infinite causal chains

I wrote a One Minute Case Against the Cosmological Argument in 2007, but looking back, I would put it simply as:

Infinities do not actually exist. Each specific set of entities is discrete. But the causal chain itself is not an existent. It is the set of all entities that have ever existed. That is a theoretical construct (like infinity or a singularity in mathematics) rather than a discrete set of entities that we can point to. If I walk from one side of the room to the other, my body exists in an infinite number of locations along that path during the time it takes me to do so. But it only exists in one location at any specific time.