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
- References:
- simple question
- From: "dimitris" <dimmechan@yahoo.com>
- simple question