"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/ …
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I am talking specifically about 0÷0
Like you say, it stops making sense for a÷0, with a≠0. -
OK, so it maintains a÷a = c ⇔ c×a = a for all a and c, but not a÷b = c ⇔ c×b = a for all a, b and c
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