What’s stopping mathematicians from defining a number for 1 ÷ 0, like what they did with √-1?

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What’s stopping mathematicians from defining a number for 1 ÷ 0, like what they did with √-1?

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Because √-1 gives a consistent result. Depending on how you approach it ÷ 0 can give you any number depending on how you approach it

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