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If a group of Computing undergraduates ask to explain why 3 is greater than 2, what is the best way to explain it?

When I asked the above question in the Math SE, one of the Mathematicians said this answer: "You have 3 apples. Is that more apples than 2 apples? "

This was a question asked from me at an interview, and that's exactly how I explained it. I told about cattle actually instead of apples. But one professor said we could have used the number line, in a kind of an undermining tone. This actually he did to kind of show his superiority I guess.

I said, yes, if we try to explain it using a mathematical way, we can use the number line too, I thought you were asking for a more detailed explanation, that's why I said like that. So, I know some say such comments to show their superiority. How to face such questions and comments to my answers in the future? Any suggestions please.

I mean, I don't like to feel undermined just because of he wants to show his superiority in front of everyone. I'm feeling bad that others who are not doing Maths might believe him more and have a negative feeling about me. I have the second interview soon.

So how can I use and show my Mathematical knowledge and defend myself in the future. I know there are such Mathematicians so any practices the you'll follow as academics to face such situations?

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    A fairly common interviewer strategy is to challenge whatever answer you give - they want to see how you react, and whether you can justify/defend your views.
    – avid
    Commented Oct 8, 2023 at 13:13
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    Personally, I think your answer (and the one that QY had suggested in his comment) was aiming too low. In your place, before answering, I would have asked about the level of these undergraduates. In my experience, many CE majors take classes with rigorous math proofs. For such students, your answer would be a bit insulting.
    – Moishe Kohan
    Commented Oct 8, 2023 at 16:25
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    one professor said we could have used the number line --- I don't know what I would have said in reply to the question (maybe "doesn't this depend on the order defined on the underlying set"), but in response to "could have used the number line" I would ask what if we're considering 2 and 3 as complex numbers?
    – Dave L Renfro
    Commented Oct 8, 2023 at 18:58

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I'm not sure why you should feel "undermined". Your explanation was fine. The professor's was fine. They may just have been giving an alternate explanation, not necessarily a superior one. In some courses I might have reminded you of alternative ways of looking at some (any) issue. There is nothing inherently wrong or demeaning about that.

Having written a book that includes things like the axiomatic treatment of the Natural Numbers (Peano's Axioms), it is pretty clear the the "number line" concepts evolved from simpler concepts like what you expressed (the "successor relationship"). Then later the definition of the "greater than" relation based on it.

The different explanations are really just rooted in different insights, one more complex, perhaps, but a complex explanation for a simple situation isn't necessarily "best" and using a simple explanation shouldn't reflect badly on you. If the professor thinks it does, they have a problem IMO. Especially so if they used an "undermining" tone.

In particular, the "best" way to explain anything depends on the context, including the audience.

I suggest you relax. It might be benign. But if the professor is a jerk that is their issue, not yours.

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