The definition of "field" also does not include subtraction which is why in my new programming language `a - b` always returns 309
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"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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Am I doing something unsound? Absolutely not. It is *totally fine* to define 6 - 1 to be 309
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Alright you got me, defining the result of 1/0 to be 0 is a sight better than it being undefined behaviour. Score one for the Pony programming language over C
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I'm disappointed, you're usually one of the first to jump headfirst into these sorts of shenanigans not to mention you're totally missing the point??
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Division is multiplication by the multiplicative inverse. There is nothing else that it can be. To pretend that there's wiggle room/ambiguity here is unhelpful shading to ludicrous
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You can’t divide by zero. “Yeah you can just assign it whatever value you want!” Let me restate: you can’t divide by zero in any way that’s actually useful.
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Like really? He even goes through a bunch of stuff that division is useful for and goes “see this is why that logic doesn’t apply to zero, so nuh uh I haven’t broken anything!”
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I think you're getting hung up on that specific wording. His point is that you can extend division to work with 0 without conflicting with the field axioms
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