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MathGroup Archive 2007

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Re: simple question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73720] Re: simple question
  • From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
  • Date: Mon, 26 Feb 2007 06:15:26 -0500 (EST)
  • References: <200702240712.CAA09136@smc.vnet.net> <4E41D3AD-48C8-446F-BFCF-7C4A731A363C@mimuw.edu.pl> <errla1$838$1@smc.vnet.net>

Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:
> Sorry, I posted not what I had intended. Let me do it all again. We
> define:
>
> I1 = Pi/2 - ArcTan[u];
> I2 = ArcTan[1/u];
>
> and want to show that I1==I2 for u>0. We check that the derivative of
> the difference is 0:
>
> In[42]:=
> FullSimplify[D[I1-I2,u],u>0]
>
> Out[42]=
> 0
>
> and not, to prove that I1==I2 for u>0 we simply need to evaluate the
> difference I1-I2 for just one suitable chosen u>0, e.g.
>
> FullSimplify[(I1-I2)/.u->1]
>
> 0

But one must be careful with that technique! Note that _everything_ above
still seems to work perfectly if the restriction u>0 is simply omitted
throughout, thereby seeming to show that Pi/2 - ArcTan[u] == ArcTan[1/u]
for _all_ u, which is, of course, false.

David


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