[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.