It is quite possible to find one’s self in a complex system demonstrating the underlying organisational, relational or dynamic referential properties of an infinite sequence without requiring the invocation of an actual material infinity. At a “whole systems” level of analysis, there are perhaps inevitable and emergent underlying organisational, relational or logically recursive principles or symmetries which emerge in which this distinction can be instructive.
In regards to its underlying organisational and relational features, a system can in some exist logically on (or as an expression of an essentially) infinite sequence without requiring the manifestation of an actual material infinity. This is interesting and suggests something about the range of freedom available to theory and mathematical, logical or systems modelling of “real world” entities and relationships.
It is quite possible to exist in a finite material context while the underlying organisational principles of that context exhibit or express infinite properties.