"Infinity" poses a ton of problems for both science and philosophy, I'm sure,

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"Infinity" poses a ton of problems for both science and philosophy, I'm sure, but I would like to ask about a very particular aspect of this problem. What ideas are out there right now about infinitely divisible time and human death? If hours, minutes, seconds, half-seconds, can be cut down perpetually, what does this mean for my "time of death"?