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  • Calculus is addition but over "measurable" domains, it is a rather natural generalization.

    Though, mathematicians do care about whether the calculation "makes sense" - that is, they care about the rigor. Which is why it may seem they invented something wild.

  • We pure mathematiciand do addition and multiplication all the time, it's just that what it represents is like, identification of module of structure sheaf.

    • Integration is just a summation, where limit is there to cover countablility!