Suppose you had a jigsaw puzzle that extended endlessly in length, width, and depth. If you remove a piece from the puzzle and throw it away, it seems as though infinity minus a finite quantity must equal less than infinity. This ignores the fact that the piece cannot be discarded since throwing it away implies that there’s a space outside of infinity – which is impossible if infinity is truly endless. But this is a thought experiment, so let’s give our imagination the benefit of the doubt and assume a piece of the jigsaw is indeed gone.
Why does infinity minus any finite quantity still equal infinity? If we’re talking about space-time in an infinite universe, the answer must surely be that the piece has been deleted from the spatial component of the cosmos yet the temporal component persists and the puzzle piece hasn’t actually been removed at all – in other words, infinity equals infinity.
The question now becomes “How does time persist – how can the past still exist, and how can what we call the present still exist in a billion years (or if time is infinite like the space it’s always united with ... eternally?)” May I suggest a mechanism for the subjective passage of time flowing from past to present to future that has an objective reality which is a familiar mechanism to people? It's the DVD we buy in stores and put in a player to watch movies.
This proposal also allows a degree of freedom to our thoughts and actions. DVDs - including the Cosmic DVD in which everyone's an actor - don't magically appear and force us to live pre-determined lives. They have writers, actors, producers, directors, people working with hair and makeup and costumes and props, etc. We don't have total freedom because we live in the Block Universe where every point in the future co-exists with, and influences,the present - compelling our thoughts and actions to follow the path which leads to the future.