Well, why not? The usual answers boil down to either an appeal to
arithmetic intuition (e.g. treating division as repeated
subtraction, you can never subtract zero to get anywhere) or
definition (you can't divide by zero because zero is defined not to
have a multiplicative inverse, i.e. "because I said so"). But the
former is mathematically naïve and the latter is unsatisfyingly
circular. So let's dig in to *why* we want to define zero out
of division.

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