On pp. 68 & 69 of Quentin Smith's article "Infinity and the Past" (Philosophy of Science, Vol. 54, No. 1, Mar., 1987, pp. 63-75) he wrote,
[Re: The possibility of an infinite past] The second argument is the one upon which [William Lane] Craig relies most heavily: if all possible negative numbers have been matched with past events, no new past events can be assigned to this collection. However, new assignments can be made if with the arrival of each new event in the past, each negative number is reassigned by being matched with the event immediately earlier than the event to which it had been assigned; such that, -3 is reassigned to the event to which -2 formerly had been assigned, and -2 to the event to which -1 had been assigned, and so on for all the negative numbers greater than -3. This leaves -1 free to be matched with the event that has newly become past.... [A]leph-zero [the actual infinite] plus 1 equals aleph-zero. Consequently, since there are aleph-zero past events at both times, and since there are aleph-zero negative numbers, there is no past event at either time that is unmatched with a negative number.
Craig usually illustrated his argument by using a library analogy. That is why the figure refers to books, not events.
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