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1/0 = 0 (2018)

Have a tweet: img {border-style: groove;} I have no idea if Pony is making the right choice here, I don’t know Pony, and I don’t have any interest in learning Pony.1 But this tweet raised my hackles for two reasons: It’s pretty smug. I have very strong opinions about programming, but one rule I try to follow is do not mock other programmers.2 Programming is too big and I’m too small to understand everything.

So in this post I’d like to clearly, formally lay out why it’s consistent to say that 1/0 = 0, why some of the common objections don’t apply, and what the real mathematicians say. This is a common mistake a lot of people made: assuming that some property of division is somehow part of the definition, not something we have to show is true. In general, I aesthetically “dislike” definitions and theorems that explicitly include a dependence on a function’s domain, because it leads to “side effects” when we extend them.

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