In the spirit of

Can we finally kill 0.999=1?,

Can we finally "kill" (read: "lock") "Do complex numbers really exist?" ?

  • $\begingroup$ Actually, my wife asked me a variant of this question - saying that she can't relate to complex numbers since she can't "see" them. The thread has helped me, particularly I haven't thought about the idea of denoting it as a pair with arithmetic defined on it, and later identifying (0,1) with i. Simple, but effective. $\endgroup$ – KalEl Aug 24 '10 at 11:17
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    $\begingroup$ I think if you change the title it's actually a good question. (The title is very silly though, and it is a shame that it is named so badly) $\endgroup$ – anon Aug 24 '10 at 13:12
  • $\begingroup$ See Can we finally kill 0.999...=1? for the reasons to kill and the effective handling (by Katie Banks) of a question such as this that has very likely received all of the useful answers it possibly could - but is still worth keeping around. $\endgroup$ – Tom Stephens Aug 24 '10 at 13:45
  • $\begingroup$ To what extent would you be satisfied filtering out questions tagged [philosophical]? $\endgroup$ – Larry Wang Aug 25 '10 at 0:00
  • $\begingroup$ @Kaestur: Thank you for the filtering suggestion. I am satisfied with the outcome of the conversation thus far - I really just wanted to ask the community and enough have chimed in (or remained silent) in support of leaving this question untouched at this point. $\endgroup$ – Tom Stephens Aug 25 '10 at 2:15
  • $\begingroup$ My choice of language apparently had some unforeseen backlash :/ $\endgroup$ – BBischof Aug 25 '10 at 4:28
  • $\begingroup$ Related question: math.stackexchange.com/questions/199676/… $\endgroup$ – Nick Alger Dec 7 '12 at 15:20

Why? Some folks (including I) spent significant time to give thoughtful replies.

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    $\begingroup$ So just lock it, i.e. no one can change and bump it anymore $\endgroup$ – Tobias Kienzler Aug 24 '10 at 7:11
  • $\begingroup$ Of course, and their efforts (and yours) are extremely useful. The action taken on 0.999=1? was intended to preserve the replies but lock it to keep it from collecting more responses - as it is unlikely that more responses will add anything useful at this point. $\endgroup$ – Tom Stephens Aug 24 '10 at 13:43
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    $\begingroup$ Why do you think that future replies are unlikely to add anything useful? I think future members might have much of interest to say. I don't think the thread should be closed, locked, or restricted in any way. $\endgroup$ – Bill Dubuque Aug 24 '10 at 21:00

It could be protected, to put a 10 reputation threshold for the new answerers. But I disagree that it needs to be locked or closed, for the moment.


Kill it because it's poorly conceived. In what sense do real numbers "exist" anyway? Do ordinary people even understand what is meant by cauchy-completeness? The ordinary examples of real nonrational numbers are still zeroes of polynomials with coefficients in Q (algebraic). In what sense does the quantity $\pi$ "exist"?

The idea that the real numbers are a totally concrete concept is really just a misunderstanding of the facts. In the same way that $pi$ is defined to be a solution to the pair of simultaneous equations cos(x)=-1, sin(x)=0 up to integral multiplication, $i$ is defined to be a solution to the equation $x^2+1=0$.

  • $\begingroup$ why downvote? I upvoted back. Sometimes such questions about mathematical meaning of something is just vague, and I agree those that holds mathematics is no more than a manipulation of rules. $\endgroup$ – Violapterin Dec 23 '16 at 4:58

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