Infinity actually pops up in the context of stream processing, since often times real computers need to process arbitrary amounts of data with finite memory res

Infinity actually pops up in the context of stream processing, since often times real computers need to process arbitrary amounts of data with finite memory resources. Sometimes the data is too big to fit into memory all at once, or maybe the data moves too slowly to all be available immediately. Because there is no upper bound to how long a stream may be, streaming algorithms tend to be designed to be able to handle infinite amounts of data which is a property that comes in handy surprisingly often.