It still works in that case, actually; you just have to pass through a singularity where the timeline is delayed infinitely many times, but the total amount of each of those infinite delays is finite. 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... = 1.

This is the answer to Zeno's paradox. A sports reporter gives an update every time Hercules catches up to where the tortoise was the last time he gave an update. All that happens is the sports reporter eventually needs to talk faster and faster and faster, and eventually try to give infinite updates right as Hercules passes the tortoise. Then the reporter's vocal chords explode, but otherwise the race proceeds as you would expect. (That is, just because a description of an event is infinitely long, does not mean the event itself is infinitely long in any sense.)

Lol yeah, that was a goof. I had Zeno’s paradox in mind and intended to choose a divergent series but accidentally used the textbook convergent one. Let’s swap it out for the harmonic series.