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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 ta
by excursionist 7y 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 https://en.wikipedia.org/wiki/Ordinal_number
- mikorym 7y agoIt not about historical order, it's about the order in which you need things to build upon mathematically.
- excursionist 7y agoYou don't need set theory for numbers, enumeration or arithmetic.
- mikorym 7y agoYou 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 https://en.wikipedia.org/wiki/Natural_numbers_object