Two men, identical twins, died at the same time and went to the stereotypical Christian Heaven. There, St. Peter explained that due to a clerical error, they could not be told apart. What was worse, only one of them was to be allowed in! The other would have to burn in Hell. Peter said, "however, we've come up with a solution that we think is equitable. You," he said, pointing to one of the twins, "will go to Hell for eternity. But every February 29th, you will change places with your brother for the day." The man was indignant. He cried "that's terrible! You mean that I might deserve to go to heaven, but my brother will go there and I'll only get out one day every four years?" St. Peter calmly responded, "that's correct, but in the long run you'll spend the same amount of time in both places.
This story serves to illustrate the difficulty arising from the equivalence of different sets that have the same number of elements as aleph-null, or the number of integers. Also, generally, the absurdity of instantiating an infinity of any empirical quantity such as time.

note: I did not invent this joke, but I don't know its origin