In the year since I wrote this post, Pony added partial division. I still don’t know anything about the language but they’ve been getting grief over this post so I wanted to clear that up.
I think Hillel's post was just saying that 1/0 == 0 doesn't lead to any mathematical contradictions.
Another way to think about it is that I believe 1/0 == 42 and 1/0 == 43 are just as valid. They don't lead to contradictions.
[In ZF set theory] Since 0 is not in the domain of recip, we know nothing about the value of 1 / 0; it might equal √2, it might equal R, or it might equal anything else.
But I don't think you want to use a language where 1/0 == 42, and likewise for 0.
In the year since I wrote this post, Pony added partial division. I still don’t know anything about the language but they’ve been getting grief over this post so I wanted to clear that up.
https://tutorial.ponylang.io/expressions/arithmetic.html#par...
I think Hillel's post was just saying that 1/0 == 0 doesn't lead to any mathematical contradictions.
Another way to think about it is that I believe 1/0 == 42 and 1/0 == 43 are just as valid. They don't lead to contradictions.
[In ZF set theory] Since 0 is not in the domain of recip, we know nothing about the value of 1 / 0; it might equal √2, it might equal R, or it might equal anything else.
But I don't think you want to use a language where 1/0 == 42, and likewise for 0.