Re: simple question
- To: mathgroup at smc.vnet.net
- Subject: [mg73705] Re: simple question
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Mon, 26 Feb 2007 06:07:16 -0500 (EST)
- References: <20070225101155.493$AH_-_@newsreader.com>
On 25 Feb 2007, at 16:11, David W. Cantrell wrote: > [Message also posted to: comp.soft-sys.math.mathematica] > > 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 Yes, indeed. A combination of Mathematica and mathematics can be very powerful. Alone each has its limitations, but using Mathematica without paying attention to mathematics can be dangerous. Andrzej Kozlowski