Wikipedia:Reference desk/Archives/Mathematics/2007 September 21

= September 21 =

Sign Diagrams
Hi, semi-continuation of the Binomial question: I was looking at that sheet, and I'm wondering, how do I solve an inequality through sign diagrams?? Typing "sign diagrams" in wikipedia turns up nothing. --24.76.248.193 04:52, 21 September 2007 (UTC)


 * If you have to solve, for example, the inequation f(x) < g(x) for x, you can equivalently solve > 0, or, putting h(x) := , the inequation h(x) > 0. So if you can find an argument for which function h returns a positive value, you're done. A web site explaining about sign diagrams can be found here.  --Lambiam 08:08, 21 September 2007 (UTC)

Thanks Lambiam. Tell me, how did you find websites like that? --24.76.248.193 02:25, 22 September 2007 (UTC)


 * By entering "sign diagram" into the Google search box and hitting the button labelled "Google Search". --Lambiam 11:33, 22 September 2007 (UTC)

Was it Google?? I went up to page 20 and I still couldn't find it! Major props for finding it! --24.76.248.193 05:16, 25 September 2007 (UTC)


 * For me it was entry #18 in the results of this search. --Lambiam 21:32, 25 September 2007 (UTC)

mathematical fallacy
erm, really I've got this obvious non-truth here, and it appears to stem from taking logs of something to the power ni but I wasn't aware that was a bad mathematical step to take, any explanations? $$\mathit{e}^{\pi \mathit{i}} = -1\,$$ $$\mathit{e}^{2 \mathit{n} \pi \mathit{i}} = 1, \mathit{n}\in\mathbb{R}$$ taking natural logs leaves $$2 \mathit{n} \pi \mathit{i} = 0, \mathit{n}\in\mathbb{R}$$ this obviously proves n = m for any integers n and m in the real number set, so whats wrong? ΦΙΛ Κ 20:53, 21 September 2007 (UTC)


 * Short explanation is that the exponential function maps multiple values in the complex plane to the same image, and so its inverse, the complex logarithm, is a multivalued function. Gandalf61 21:05, 21 September 2007 (UTC)
 * The even shorter explanation: When dealing with complex numbers, taking logs is a bad step. -- Meni Rosenfeld (talk) 18:21, 22 September 2007 (UTC)

Amongst other things - wheres m ?87.102.17.252 15:16, 23 September 2007 (UTC)
 * The OP has spared us some mundane details. Since $$e^{2n\pi i} = 1$$ for every $$n \in \mathbb{Z}$$, for $$n,m \in \mathbb{Z}$$ we have $$e^{2n\pi i} = 1 = e^{2m\pi i}$$, so "taking logs" gives $$2n\pi i = 2m\pi i$$ and $$n=m$$.
 * He did, however, have a different mistake; it should be $$n \in \mathbb{Z}$$, not $$n \in \mathbb{R}$$. -- Meni Rosenfeld (talk) 15:31, 23 September 2007 (UTC)
 * Such as $$\mathit{e}^{2 \mathit{n} \pi \mathit{i}} = \mathit{e}^{2 \mathit{m} \pi \mathit{i}}$$ when n=1,m=2 so therefor n=m X
 * the error in resoning could be explained in terms failure to notice the oscillating value of eix..87.102.17.252 16:02, 23 September 2007 (UTC)