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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