Of course, your very last sentence is absolutely true, but it is more part of research duties rather than teaching ones. At least, unlike teaching, you are not repeating the same thing again and again.

Dear Manfred. Could you please have a look at the revised version of the question? I think my original wording was misleading.

@ToddTrimble Can I ask in the other site while my question is still here? Or, I have to delete this one?

@ToddTrimble You are right. It is better to change "natural" to "positive". Yet, my question means all axes be positive. That is why I am not sure whether Jim's example works or not. Perhaps, I've used "natural" since we usually mark the axes with units. And, thanks for introducing the other site. I'll try it.

@ToddTrimble No, I exactly meant natural numbers (including zero): 0,1,2,.... Indeed, I guessed the problem that might arise for a modern mind, that is why I added the Sawyer's paper.

@AndrejBauer Dear Andrej. Now after more than a year I'm coming back to this question and your wonderful answer. In particular, this time what has attracted my attention is the possibility of an educational use of this claim that "proofs and computation are intimately connected, and that every time you prove something you have also written a program, and vice versa". Is there any good expository read that you might suggest? I want to explore the potential of using that claim when we teach proof.

I guess when you get one or two answer there is no way to delete the question any more. No worry. Let it go as it is

Absolutely, it is!

It seems that you practically asking people to count the number of years in each of the answers of this question:mathoverflow.net/questions/35468/…