"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/ …
I'm okay with accepting that we're not working in a field anymore, we're programming. IEEE 754 defines division, particularly division by 0 in a very consistent, useful way But then why all the distracting lies about fields, why mention them at all
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because they're not lies! all the proofs still work- 1/0=0 just defines *strictly more* things the 0^0 comparison in one of the quotes is a very apt analogy
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"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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