In the spirit of
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$\begingroup$ 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. $\endgroup$– KalElAug 24, 2010 at 11:17
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2$\begingroup$ 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) $\endgroup$– anonAug 24, 2010 at 13:12
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$\begingroup$ 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 StephensAug 24, 2010 at 13:45
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$\begingroup$ To what extent would you be satisfied filtering out questions tagged [philosophical]? $\endgroup$– Larry WangAug 25, 2010 at 0:00
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$\begingroup$ @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 StephensAug 25, 2010 at 2:15
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$\begingroup$ My choice of language apparently had some unforeseen backlash :/ $\endgroup$– BBischofAug 25, 2010 at 4:28
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$\begingroup$ Related question: math.stackexchange.com/questions/199676/… $\endgroup$– Nick AlgerDec 7, 2012 at 15:20
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3 Answers
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Why? Some folks (including I) spent significant time to give thoughtful replies.
answered Aug 24, 2010 at 5:12
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3$\begingroup$ So just lock it, i.e. no one can change and bump it anymore $\endgroup$ Aug 24, 2010 at 7:11
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$\begingroup$ 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. $\endgroup$ Aug 24, 2010 at 13:43
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5$\begingroup$ 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. $\endgroup$ Aug 24, 2010 at 21:00
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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.
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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 $x^2+1=0$.
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$\begingroup$ 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. $\endgroup$ Dec 23, 2016 at 4:58