[Tainnor]

Mathematicians not working in type theory generally agree that 1/0 is undefined (or if anything, they would set it to infinity, but even saying that would probably be too cavalier for most mathematicians). They do not necessarily for 0^0. There are good algebraic and combinatorial reasons for 0^0=1, while analysts will complain about non-continuity.

[klodolph]

I think that’s missing the point. What I’m saying is “this is a convention, and because it is a convention, it may be reasonable to follow a different convention at times”. Different conventions are convenient for mathematicians working in different fields. Whether a convention is “semantically correct” is not a question that even makes sense, because when you define something, your definition is true by definition. The only real question here is whether you can reasonably expect people to understand you if you use different definitions.

[Tainnor]

This is a view of mathematics and programming that just completely ignores intuition. Of course, what you say is technically correct, yet mathematicians debate definitions all the time, precisely because it matters to them to get them "right" (of course, there's rarely one true answer).

This is even more true in programming. Yes, you can also learn all the type conversion rules of JavaScript, but many people agree that they are insane because they violate the principle of least surprise. Expectations matter, especially when you're fixing a bug at 3am.

[klodolph]

Intuition is mostly an internalized notion of convention, and I don’t think that we can appeal to intuition to resolve much.

For students learning division, the fact that 1/0 is undefined is not an intuitive result and must be learned. This is their first time encountering something which is “not defined”.

[Tainnor]

We'll just have to disagree about this. I think intuition is incredibly important both in mathematics and in programming.

[klodolph]

We agree that intuition is important, I think we disagree about where it comes from. Intuition comes from experience. A programming language is “intuitive” because it conforms to your previous experiences with programming languages.