Those are all just normal imaginary numbers. The question is why, when we can't answer a question, we don't just invent a symbol, say it's the answer to the question, and call it a day.

It's a stupid question, but it's not related to your response.

The question has 300+ upvotes. That’s a proxy for how “good” it is. A person is curious about an aspect of mathematics and posed a well stated question. It is not a stupid question. From their perspective mathematicians appear to do something and they wonder why it can’t be done in other situations. Such a question is the basis of understanding. It is by wondering such things that enables one to gain true understanding of a topic.

Most questions asked by beginners in an area are “stupid” and few as insightful as this one. I’ve taught mathematics at a community college for 20 years and I would be delighted to have been asked this. Usually questions are mundane like, “Why did you add x to both sides?”. Here the person is trying to understand what mathematicians do, what the basis of expanding a number system really involves. This is a fantastic question.

Peoples’ curiosity ought not be labeled as stupid.

> Peoples’ curiosity ought not be labeled as stupid.

Correct. That is why I feel more comfortable asking "stupid" questions to chatGPT. I clarified a lot of concepts in economics through repeatedly asking questions about each concept that pop up in its answers and trying to push it to the limits of what can be defined, explained, etc. One cannot be sure of the truthfulness or soundness of the answers, but they may help.

> It is not a stupid question. From their perspective mathematicians appear to do something and they wonder why it can’t be done in other situations.

I mean, you've already gotten it wrong. This can be done in other situations. Where it isn't done, it isn't done because doing it is pointless, not because there's some bar to giving names to opaque labels.

How does your pedantry contribute meaningfully?

If something doesn’t behave like 0 in a ring or other algebraic structure then using that label is confusing and simply not done. You are free to use any symbol you want but mathematics is a human endeavor and as such communication is important. Using the symbol 0 signifies something to those with mathematical training. Zero can’t have an multiplicative inverse because anything you call 0 that has an multiplicative inverse makes it behave like something other than zero. So no one would use 0 to describe such an element. In a ring, or abelian group, the symbol 0 is reserved for the additive identity element.

Similarly, I could say snkwoo is what most people call a chair. A grammarian would say there is no word snkwoo even though I just defined it.

Your original comment was wrong and bad. Instead of just admitting it or moving on you’ve decided to double down and make another bad comment.

I'm having trouble following the argument from your premise "it is a stupid question to ask why I referred to a chair as a chair instead of a snkwoo" to your conclusion "it is not a stupid question to ask why, when we have no answer to a question, we don't just say that we do have one".

The answer (to both of those questions!) is, of course, that we could do that, but it wouldn't accomplish anything. Asking the question just means you have no idea what you're saying. Or in other words, it's a stupid question.

> Please don’t become a teacher.

I've been one!

Interestingly, the most consistent comment I got, from both students and school administration, was "you're so patient with the students".

Try humoring me. Did I describe your premise accurately? Did I describe your conclusion accurately? How do you get from one to the other?

A child asked her mother, “Can I put my hand in the fire?”. The mother responded, “That’s a stupid question. Of course you can.”. The child put her hand in the fire and got severe burns on her hand. She learned then that instead asking “Can I…” she should have asked, “Is it advisable…”. Unfortunately for her she lived in a society in which people frequently say things like, “You have to file taxes on or before April 15.” when they mean, “You can file taxes after April 15 but you may incur fees and penalties if you do so.”. She later became a teacher and was very patient with her students.

> Asking the question just means you have no idea what you're saying. Or in other words, it's a stupid question.

So, to be clear, you're saying that the only kind of question that isn't stupid is the one where the querent already has perfect knowledge of the discipline?

I'm saying that to avoid asking a stupid question, you need to know the meaning of your own question. Stringing words together at random isn't going to get you there.

Compare the famous anecdote from Charles Babbage:

On two occasions I have been asked, -- "Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?" [...] I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.

Is it necessary to have perfect knowledge of the workings of the Difference Engine to avoid asking that question? Of course not. Any knowledge at all would do the trick. If you put gravel into a water mill instead of grain, will you still get flour out of it?