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by excursionist 2292 days ago
Set theory constructs the natural/ordinal numbers from it's axioms, but set theory is a man-made formal language that didn't exist until the 19th century, so talking about what comes/before after is kind of moot.

https://en.wikipedia.org/wiki/Ordinal_number

1 comments

It not about historical order, it's about the order in which you need things to build upon mathematically.
You don't need set theory for numbers, enumeration or arithmetic.
You don't need it, but sets are more primitive than numbers.

For example, the category of finite sets without an NNO [1] is simpler or more foundational than the set of natural numbers. At the same time, this category is actually a category of numbers.

My point is that numbers are complicated by nature, but they are more intuitive for humans (mostly I think) than sets are. Sets are simpler or more basic, but often less intuitive for humans.

[1] https://en.wikipedia.org/wiki/Natural_numbers_object