Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2007
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2007

[Date Index] [Thread Index] [Author Index]

Search the Archive

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


  • Prev by Date: Re: Symbol name extraction
  • Next by Date: Re: Re: reliability function drawing
  • Previous by thread: Re: simple question
  • Next by thread: deleting a title or subtitle in a notebook