From Wikipedia, the free encyclopedia

Mathematics desk
< September 20	<< Aug | September | Oct >>	September 22 >

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

Contents 1 September 21 1.1 Sign Diagrams 1.2 mathematical fallacy

[edit] September 21

[edit] 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 g(x) – f(x) > 0, or, putting h(x) := g(x) – f(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)

[edit] 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?


taking natural logs leaves

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^2nπi = 1 for every , for we have e^2nπi = 1 = e^2mπi, so "taking logs" gives 2nπi = 2mπi and n = m.

He did, however, have a different mistake; it should be , not . -- Meni Rosenfeld (talk) 15:31, 23 September 2007 (UTC)

Such as e^2nπi = e^2mπi 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 e^ix..87.102.17.252 16:02, 23 September 2007 (UTC)