[lolcatuser]

You're being willfully obtuse here.

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.