"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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math is about formal systems. the post cites at least two other variants that do something else useful with division by 0. it makes the case for why 1/0=0 is useful in some scenarios. why the mockery?
In a field, division is multiplication by the multiplicative inverse. You can redefine "division" to mean something else if you like but you're probably either no longer working in a field or no longer speaking conventional mathematical English
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absolutely, the post is rather clear on that point- and leaving behind "conventional mathematical English" is a fairly common thing to do but also, to be fair, this is less a redefinition and more an extension
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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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