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Invented. Math holds no bearing on reality.
9, 3*3, 3^2, and ||||||||| all represent different ideas within the concept of "numerical object", which we call numbers. They are not the same.
5, 3/2, sqrt(2), and pi all represent different ideas within the concept of "numerical object", which we call numbers. None of them exist beyond symbols on a page, as math and physics hold no bearing on reality.
Some will assert that "irrational numbers" are not numbers. That doesn't matter, because irrationals are "numerical objects", which many people call numbers.
Large integers do not exist in a unary notation, like 10^100. Large integers do not exist in positonal notation, like 10^10^100.
A program converting 10^100 into unary notation will not terminate due to physical limitation, per Bremermann's Limit. Do not trust the axiom of induction.
The natural numbers do not exist in totality. There is no largest number. We continue to construct larger numbers.
