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Alon Amit's answer to Could we 'invent' a number [math]h[/math] such that [math]h[/math][math]={{1}\over{0}}[/math], similarly to the way we 'invented' [math]i=\sqrt{-1}[/math]? What would be the effect on modern math if we did so? - Quora
You may not be aware of this, but mathematicians are very imaginative and creative people. They love defining new things, they love analogies, they love challenging accepted assumptions and they love completeness and symmetry.
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