I think you both need to watch some YouTube math videos on what exactly infinity means. As Everyday Maths put it, it’s not “count until you can’t count anymore and then add one to the number”. That’s the sort of wrong frame of thinking that makes you think that an infinite pile of hundred dollar bills is worth more than an infinite pile of one dollar bills. They are both worth $infinity.
We don’t have any algorithms that can deal with infinity, so stop pretending like we do. And we couldn’t build one unless the universe is infinite and expansions turns out to be incorrect. So no infinity in computer data structures.
When somebody says "this algorithm is unbounded" they of course don't mean that they've changed the laws of the universe to allow for an infinite array of memory that it can work with. They just mean that if you could do that, it'd work.
As an example: `while (node) node = node->next;` (in C, where `node`'s type defines a reference to `next` of the same type) will traverse an unbounded list. It will work just as well for zero nodes, one node, a dozen nodes, a billion nodes, and so on, as the number of nodes approaches infinity. Obviously it is impossible for you to ever create a computer with an unbounded amount of memory, but computer scientists can talk about algorithms the same way mathematicians can talk about what `f(x)=x^2` at infinity.
No mathematician, with the knowledge we have now, would ever say, "It's unreasonable for us to talk about infinity. That's simply not possible, ever, now or in the future, so let's limit things at 999,999,999,999,999,999,999,999,999." We settled this debate back in the 1600s.
