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I am sorry if this question is off-topic here. This is not really a question, but more a request to provide examples of un-real numbers.

So far I know only one example that I will put in the list below.

However, to justify this post, I will yet ask this: Would it be correct to say that an un-real number is not a number at all, but rather some kind of concept of a phenomenon that simply doesn't exist in the objective reality?


List of examples of un-real numbers:

  1. Any square root of any negative number;

  2. ?

brilliant
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This ultimately just comes down to playing with definitions. What exactly do you mean by a number? If you mean a member of ${\mathbb{C}}$, then by an "un-real" number, assuming you mean a number that is not strictly real, that is precisely the set ${\mathbb{C}\setminus \mathbb{R}}$. Otherwise, without a precise definition of what exactly you are talking about, the question is ill-posed.

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    Why answer ill-posed questions? The normal procedure at MSE is to ask for a clarification and if none is forthcoming, then vote to close. – Moishe Kohan Feb 23 '22 at 01:45
  • I am sorry. I thought there was a precise definition of unreal number in math. – brilliant Feb 23 '22 at 01:50
  • @MoisheKohan because I think giving an answer that the question is ill-posed is still a valuable answer, especially because questions of this sort usually imply there is some notion of a number outside of an abstract definition depending on the current context. It's essentially just word-play, and I think any opportunity to point out such word-play is definitely one worth taking – Riemann'sPointyNose Feb 23 '22 at 01:51
  • @brilliant no need to be sorry, now you know! – Riemann'sPointyNose Feb 23 '22 at 01:51
  • @brilliant maybe you would be interested in looking at Quaternions, though, as these are closely related to complex numbers – Riemann'sPointyNose Feb 23 '22 at 01:53
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    @Riemann'sPointyNose: Are you aware of EOQS? If not, please, read closely. – Moishe Kohan Feb 23 '22 at 01:57
  • @Riemann'sPointyNose - I'll look at Quaternions. Thank you. – brilliant Feb 23 '22 at 01:59
  • This should be a comment, as it does not answer the question. As @MoisheKohan points out succinctly, seek clarification, give feedback/suggestions for clarification, in comments below a question. Only answer if and when you fully understand the question. – amWhy Mar 04 '22 at 22:34