"The field definition does *not* include division. This means we are free to define division however we want" is one of the stupider things I've read todayhttps://www.hillelwayne.com/post/divide-by-zero/ …
"The field definition does not include division, nor do our definitions of addition or multiplication. This means we are free to define division however we want" is a lie
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nope the post goes into this- division is *conventionally* multiplication by the inverse, but that's extra. and note that, when the inverse exists, that's still true here anyway. but at this point you're just arguing tangential trivialities
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In a field, division is always multiplication by the multiplicative inverse. This is universally understood and unambiguous
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