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MathGroup Archive 2004

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Re: Re: how to explain this weird effect? Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46327] Re: [mg46290] Re: how to explain this weird effect? Integrate
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 14 Feb 2004 04:38:04 -0500 (EST)
  • References: <200402121216.HAA12039@smc.vnet.net> <c0hhvb$lgl$1@smc.vnet.net> <200402140256.VAA08500@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 14 Feb 2004, at 03:56, steve_H wrote:

>
> mathematically speaking, 1/a when a=0, is the same as Limit[1/a , a->0]
> So, the final answer should not be different.
>
>
Really? If so then for over 20 years I have teaching it all wrong, and 
so have all other professional mathematicians for much longer. If the 
limit of a function at a point is just the value of that function then 
why do we need to concept of limit at all?
In fact, Mathematica does not return the same answer in both cases, 
since Infinity and ComplexInfinity are not the same thing in 
Mathematica.

Quite apart from that, the order of evaluation is a key issue in 
functional programming languages and there are lots of cases where 
Mathematica will produce different answers if you change the order of 
evaluation even if "mathematically" you are computing the same thing.


Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/


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