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> A set of dates obviously has an earliest date.

Uhh, no you’re thinking in terms of a finite set. From the set of all dates, what’s the latest possible date, or conversely the earliest possible date. The temptation is to say infinite BC is the earliest possible date, but infinity is not a number.

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> infinity is not a number

Infinity is not a number, it's a set of numbers, but specific infinities (e.g., the cardinality of the natural numbers, aleph-naught) are individual numbers, just not finite numbers.

But there is no infinite BC, right? There cannot be any date earlier than the date of the big bang. That establishes a lower bound for the set of dates, does it not?

The Big Bang is an apparent discontinuity, but we have no idea if a universe existed before this one. Alternatively, multiple universes could exist and those alternate universes could be much older. So at least theoretically things much older than our universe could exist.

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