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A comment on American parents are sending their kids to 'Russian math' (2017). Parent comment
In a universe with more than one object, cardinality exists. Natural numbers are how we can discuss cardinality.
Natural numbers are also how we discuss ordinality, because ordinality exists in any universe having at least one dimension.
Axioms are how we discuss natural numbers rigorously. But natural numbers exist independent of any axioms. That's why they're called natural numbers
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In a universe with more than one object, cardinality exists. Natural numbers are how we can discuss cardinality.
Natural numbers are also how we discuss ordinality, because ordinality exists in any universe having at least one dimension.
Axioms are how we discuss natural numbers rigorously. But natural numbers exist independent of any axioms. That's why they're called natural numbers